Last visit was: 21 Jul 2024, 21:34 It is currently 21 Jul 2024, 21:34
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Difficulty: 555-605 Level,   Geometry,               
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94441
Own Kudos [?]: 642840 [48]
Given Kudos: 86716
Send PM
Most Helpful Reply
examPAL Representative
Joined: 07 Dec 2017
Posts: 1048
Own Kudos [?]: 1799 [9]
Given Kudos: 26
Send PM
examPAL Representative
Joined: 07 Dec 2017
Posts: 1048
Own Kudos [?]: 1799 [5]
Given Kudos: 26
Send PM
General Discussion
Intern
Intern
Joined: 06 Apr 2019
Posts: 29
Own Kudos [?]: 40 [5]
Given Kudos: 24
Location: India
Concentration: General Management, Healthcare
WE:Consulting (Consulting)
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
3
Kudos
2
Bookmarks
Answer should be D. Both together are sufficient.

The pictures shows its a right angled triangle

1. Z= 13. Since its right angled, \sqrt{\(x^2+y^2\)} =13 => \(x^2+y^2\) = 169

Alone not Enough

2. A= 5y/2

Area of triangles = 1/2bh => SInce its right angled, in this case A= x*y/2

xy/2 = 5y/2 => x=5. We still need value of X. Hence this option is alone not enough

Together used, we can determine value of "Y" by substituting "X" value in Eq1 => \(y^2\) = 169-25 = 144
=> y= 12. Hence A= 30
Manager
Manager
Joined: 18 Feb 2018
Posts: 83
Own Kudos [?]: 26 [4]
Given Kudos: 1297
Location: India
Concentration: International Business, Economics
GPA: 3
WE:Law (Telecommunications)
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
4
Kudos
A is sufficient alone. first of all 144 + 25 = 169. secondly, we have to find A it does not matter whether we are able to find the X and Y.

12*5*(1/2)=30

regardless of the height and length.
Manager
Manager
Joined: 19 Jan 2019
Posts: 82
Own Kudos [?]: 58 [0]
Given Kudos: 8
GMAT 1: 650 Q49 V30
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
DavidTutorexamPAL wrote:
The Logical approach to this question would start off with the pythagorean theorem: a²+b²=c². Since this is one equation with three variables, statement (1) on its own is not enough to solve it. Answer choices (A) and (D) are eliminated.
Statement (2) relates to the formula of the area of a right triangle, which is the product of its legs divided by 2. Since we know that one leg is y and the area is 5y/2, we have enough information to find x, but not for any of the other sides. Answer choice (B) is also eliminated.
Using both statements, if we have both x and z, we can find y, and thus have enough information to calculate the area. The correct answer is (C).

Posted from my mobile device


Hey David... According to each statements, is it wrong to conclude that it's a 5-12-13 right angle traingle... Is it a trap??
Manager
Manager
Joined: 23 Jul 2015
Posts: 66
Own Kudos [?]: 29 [0]
Given Kudos: 297
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
Hi! I am confused. Why can't the answer be A? If the hypotenuse is 13 then the right angle triangle has to be a 5-12-13. We have the Base and Height to figure the area.
Manager
Manager
Joined: 31 Mar 2019
Posts: 87
Own Kudos [?]: 57 [1]
Given Kudos: 105
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
1
Kudos
SPatel1992 wrote:
Hi! I am confused. Why can't the answer be A? If the hypotenuse is 13 then the right angle triangle has to be a 5-12-13. We have the Base and Height to figure the area.


Hi Spatel1992 / All ,

Finally I got the answer , here it goes

Initially , I also thought that the only answer that goes with hypotenuse 13 would be 5,12,13 but later on , I found something interesting.

There is another pythagoras triplet with 13 and that’s 13,84,85 ......

Hope this helps :)

Posted from my mobile device
Manager
Manager
Joined: 30 Jan 2020
Posts: 141
Own Kudos [?]: 147 [2]
Given Kudos: 143
Location: India
GPA: 4
Send PM
If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
2
Kudos
Bunuel wrote:

If A is the area of a triangle with sides of lengths x, y, and z as shown above, what is the value of A ?

(1) z = 13
(2) A = 5y/2


Attachment:
2019-04-26_1842.png



Hey guys!

Hope this explanation proves to be valuable for all!

1. Statement 1 says that z=13,
Yes, we do know that there is a Pythagorean triplet for this question- '12,5,13'.
But we cannot conclude on this as there can be alternate measures as well.
So, Drop Statement 1 for now

2. Statement 2 says that \(Area(A)= \frac{ 5y}{2 }\)
So, we can conclude saying that the value of x=5,
Because, \(Area of Triangle= \frac{1}{2} * x * y \)
So, A= 2.5y

We cannot go further on this, as the information is insufficient.

Combining statements 1 and 2,
We get to know the 2 values, i.e., x=5 and z=13
We finally accomplish the values for this triplet!
z^2= x^2 + y^2

And, we shall find the Area of triangle using the standard formula.

Official Answer:- Option C

Hope this helps you friends! saarthakkhanna04 SPatel1992 manu11 thyagi anilesh10 LeenaSai UNSTOPPABLE12 digvijayk1


Thank you!

Regards,
Raunak Damle :cool:
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11479
Own Kudos [?]: 34505 [2]
Given Kudos: 323
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
2
Kudos
Expert Reply
Bunuel wrote:

If A is the area of a triangle with sides of lengths x, y, and z as shown above, what is the value of A ?

(1) z = 13
(2) A = 5y/2

DS20602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
2019-04-26_1842.png



Area = \(\frac{1}{2}*x*y\)

1) z=13
So x^2+y^2=13^2
As we are not told x and y are integers, we will have numerous (x,y) fitting in.
For every real value of x<13, there will be a value for y. Although integer value will be just (5,12) or (12,5)
x=1.....\(y^2=169-1=168\)....\(y=\sqrt{168}\)
Insuff

2) A=5y/2
A=xy/2=5y/2......x=5
But nothing about y

Combined
x=5.....\(5^2+y^2=13^2......y=12\)
Area = 5*12/2=30
Suff

C
Director
Director
Joined: 28 Sep 2018
Posts: 710
Own Kudos [?]: 573 [1]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Send PM
If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
1
Bookmarks
Bunuel GMATBusters please could you confirm the following notes that I have made so far on right-angled triangles:

"1. If we have a triangle with sides in the ratio 3: 4: 5 (of any triplet) THEN by default the triangle is 90°

2. If we have a triangle with two sides in the ratio 3: 4 and even if we know it is a 90° triangle WE CANNOT assume the third side to be a multiple of 5 (or any such triplet sequence)

3. If we are told that the triangle is 90° AND one of its legs is 1/2 the hypotenuse, THEN the triangle is 30°- 60° - 90° "
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1895
Own Kudos [?]: 5797 [1]
Given Kudos: 238
WE:General Management (Education)
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
1
Kudos
Expert Reply
"1. If we have a triangle with sides in the ratio 3: 4: 5 (of any triplet) THEN by default the triangle is 90°.

Response : YES, it will be a right angled triangle.

2. If we have a triangle with two sides in the ratio 3: 4 and even if we know it is a 90° triangle WE CANNOT assume the third side to be a multiple of 5 (or any such triplet sequence)

Response: yes coz the sides can be (3, 4, 5) when angle between 3 and 4 is 90 deg or (3, root 7, 4) when angle between 3 and root 7 is 90 deg.


3. If we are told that the triangle is 90° AND one of its legs is 1/2 the hypotenuse, THEN the triangle is 30°- 60° - 90° "[/quote]

Response: Yes, your understanding is correct.

Hoozan wrote:
Bunuel GMATBusters please could you confirm the following notes that I have made so far on right-angled triangles:

"1. If we have a triangle with sides in the ratio 3: 4: 5 (of any triplet) THEN by default the triangle is 90°.

Response : YES, it will be a right angled triangle.

2. If we have a triangle with two sides in the ratio 3: 4 and even if we know it is a 90° triangle WE CANNOT assume the third side to be a multiple of 5 (or any such triplet sequence)

Response: yes coz the sides can be (3, 4, 5) when angle between 3 and 4 is 90 deg or (3, root 7, 4) when angle between 3 and root 7 is 90 deg.


3. If we are told that the triangle is 90° AND one of its legs is 1/2 the hypotenuse, THEN the triangle is 30°- 60° - 90° "


Response: Yes, your understanding is correct.

Posted from my mobile device
Director
Director
Joined: 28 Sep 2018
Posts: 710
Own Kudos [?]: 573 [0]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Send PM
Re: If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
GMATBusters wrote:
"1. If we have a triangle with sides in the ratio 3: 4: 5 (of any triplet) THEN by default the triangle is 90°.

Response : YES, it will be a right angled triangle.

2. If we have a triangle with two sides in the ratio 3: 4 and even if we know it is a 90° triangle WE CANNOT assume the third side to be a multiple of 5 (or any such triplet sequence)

Response: yes coz the sides can be (3, 4, 5) when angle between 3 and 4 is 90 deg or (3, root 7, 4) when angle between 3 and root 7 is 90 deg.


3. If we are told that the triangle is 90° AND one of its legs is 1/2 the hypotenuse, THEN the triangle is 30°- 60° - 90° "


Response: Yes, your understanding is correct.

Hoozan wrote:
Bunuel GMATBusters please could you confirm the following notes that I have made so far on right-angled triangles:

"1. If we have a triangle with sides in the ratio 3: 4: 5 (of any triplet) THEN by default the triangle is 90°.

Response : YES, it will be a right angled triangle.

2. If we have a triangle with two sides in the ratio 3: 4 and even if we know it is a 90° triangle WE CANNOT assume the third side to be a multiple of 5 (or any such triplet sequence)

Response: yes coz the sides can be (3, 4, 5) when angle between 3 and 4 is 90 deg or (3, root 7, 4) when angle between 3 and root 7 is 90 deg.


3. If we are told that the triangle is 90° AND one of its legs is 1/2 the hypotenuse, THEN the triangle is 30°- 60° - 90° "


Response: Yes, your understanding is correct.

Posted from my mobile device[/quote]


So following this thought process, if we were given that the triangle is 90° such that the hypotenuse is 5 and one of the sides is 4, now in this case unline in point 2, we can use the tripllet knowledge right? Since now we know that the 90° angle is between 3 and 4
Director
Director
Joined: 04 Jun 2020
Posts: 542
Own Kudos [?]: 74 [0]
Given Kudos: 623
Send PM
If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
chetan2u wrote:
Bunuel wrote:

If A is the area of a triangle with sides of lengths x, y, and z as shown above, what is the value of A ?

(1) z = 13
(2) A = 5y/2

DS20602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
2019-04-26_1842.png



Area = \(\frac{1}{2}*x*y\)

1) z=13
So x^2+y^2=13^2
As we are not told x and y are integers, we will have numerous (x,y) fitting in.
For every real value of x<13, there will be a value for y. Although integer value will be just (5,12) or (12,5)
x=1.....\(y^2=169-1=168\)....\(y=\sqrt{168}\)
Insuff

2) A=5y/2
A=xy/2=5y/2......x=5
But nothing about y

Combined
x=5.....\(5^2+y^2=13^2......y=12\)
Area = 5*12/2=30
Suff

C


chetan2u
I am so sorry to bother you with this very basic algebra question but to confirm when solving for .5bh=5y/2 --> I did xy=5y --> so then x=5 because the ys cancel out, right?

Also, the Official Answer says that at least two sides of a right triangle must be known to find the area. Doesn't this apply to ALL triangle types (in that you need at least two sides to find the area of any triangle)?

Thank you and Happy Holidays!
GMAT Club Bot
If A is the area of a triangle with sides of lengths x, y, and z as sh [#permalink]
Moderator:
Math Expert
94441 posts