Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59180

What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:00
Question Stats:
80% (01:16) correct 20% (01:22) wrong based on 345 sessions
HideShow timer Statistics
What is the area of triangle ABC above, with side lengths x, y, and z? (1) \((x+y)^2 (xy)^2=80\) (2) \((xy)= 1\)
Attachment:
Untitled.png [ 5.28 KiB  Viewed 2605 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Director
Status: Manager
Joined: 27 Oct 2018
Posts: 726
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:20
the question is asking about the value of \(\frac{x*y}{2}\) from statement (1), 4xy = 80, xy = 20, \(\frac{x*y}{2}\) = 10 > sufficientfrom statement (2), x is taller than y by 1 unit, but no constrains about the values of each > insufficientA
_________________




Manager
Joined: 31 Dec 2018
Posts: 114
Location: India

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:09
1) (x+y)²−(x−y)²=80 gives, x²+y²+2xyx²y²+2xy=80 4xy=80 xy=20
Possible values of x,y can be 4,5 or 5,4
Voila!! A is sufficient.
2. (xy)=1 could be any value. Naah... Insufficient.
So, IMO A.
Posted from my mobile device



Intern
Joined: 15 Feb 2019
Posts: 3

What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:13
(X+y)^2 (xy)^2 equals 4xy 4XY =80 XY=20 1/2 XY =10...Answer A
Statement B is good for nothing So,the answer is A Hit Like and give a kudos if u like the solution
Posted from my mobile device



Manager
Joined: 11 Feb 2013
Posts: 216
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)

What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
Updated on: 02 Jul 2019, 08:53
Question: (1/2) xy=? Here, (1/2) is fixed numerical term. So, if we find the value of xy, we can can easily find the value of (1/2) xy i.e. AREA of the triangle. SO, WE SIMPLY NEED the value of xy. Thus, question becomes xy=?
Statement 1: (x+y)^2 (xy)^2=80 => x^2+2xy+y^2x^2+2xyy^2=80 => 4xy=80 => xy=20 SUFFICIENT
Statement 2: xy= 1 Case 1: if x=2 & y=1, then xy=2, Case 2: if x=5 & y=4, then xy=20,
Not SUFFICIENT. Answer:A



VP
Joined: 19 Oct 2018
Posts: 1080
Location: India

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:18
Area of triangle = 1/2*x*y
Statement 1=(x+y)^2−(x−y)^2= (x^2+y^2+2xy) (x^2+y^22xy)=4xy=80
4xy=80 1/2*x*y=10 Sufficient
Statment 2 xy=1 We can't find x*y with the given information Insufficient
A



Intern
Joined: 10 Jan 2018
Posts: 15

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:21
Area is dependent on XY , clearly we get XY from 1 using a2b2 equals (a+b)(ab), so we get ans from A , while 2 will give a equation with infinite possible ans
Posted from my mobile device



Senior Manager
Joined: 09 Jun 2014
Posts: 351
Location: India
Concentration: General Management, Operations

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:22
I guess A is the answer for above problem.
Area= 1/2 *x*y
So we need xy.
Now simplifying equation 1 we know a^2  b^2 = (a+b)(ab)
So (x+y)^2−(x−y)^2=80
(x+y+ x−y)(x+yx+y) = 80
2x*2y= 80 xy = 20
So statement 1 is sufficient to find the area.
STAT2: (x−y)=1
we dont' know what is xy.No other information is provided.
Clearly ,STAT2 is insufficient.
So A is answer.



Manager
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:22
St 1 (x+y)^2 (xy)^2=80 => (x+y+xy)(x+yx+y)=80 => 2x*2y=80 =.xy=20 Area= 1/2xy sufficient
St2 (x−y)=1 x=y+1 x can take any value depending o value of y.not sufficient
Ans.A



Senior Manager
Joined: 31 May 2018
Posts: 451
Location: United States
Concentration: Finance, Marketing

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:24
since triangle, ABC is a rightangled triangle right angle at B
area of triangle ABC = \(\frac{1}{2}\)xy
so we need to find the value of xy
statement (1) \((x+y)^2  (xy)^2\) = 80 \(x^2+y^2\)+2xy  \(x^2y^2\)+2xy = 80 4xy =80 xy = \(\frac{80}{4}\) so from here we can find the area of the triangle so SUFFICIENT
statement (2) (x−y) = 1 from this statement, we cannot get the definite values of x and y hence we cannot get the difinite value of xy so this statement is INSUFFICIENT
correct answer is A



Intern
Joined: 29 May 2019
Posts: 32

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:24
A is sufficient to answer considering the expansion we get xy = 20 and area is 1/2*xy and triplets in B option not sufficient to answer the question
Posted from my mobile device



Manager
Joined: 27 Mar 2018
Posts: 79
Location: India

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:24
Area of triangle ABC = \(\frac{xy}{2}\) 1) Considering (x+y) = a and (xy)=b, we have a^2b^2=80 => (ab) (a+b)=80 => xy = 20 Area of ABC = 10. Sufficient 2) Given, (xy)=1 For x=5 and y=4, area of ABC=10 For x=6 and y=5, area of ABC=15 Not sufficient. Hence, answer A. IMO
_________________
Thank you for the kudos. You are awesome!



Director
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:26
i) Sufficient as when the equation is expanded gives 4xy=80; xy=20 and area of triangle is 1/2*leg1*leg2=1/2xy=10 ii)Insufficient as neither xy or individual values of x and y can be found from xy=1 IMO A
_________________
Give +1 kudos if this answer helps..!!



Manager
Joined: 24 Jan 2019
Posts: 107
Location: India
Concentration: Strategy, Finance
GPA: 4

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:27
We have to find the area of the given triangle. So, indirectly we have to see whether we can find the value of XY from the given information.
(1) Solving the given equation will give us the value of XY. So one can easily find an area of the given triangle. So, 1 can independently answer the question.
(2) Values of X, Y & Z can be fractions or integers. (We don't have enough information about them in the question)
Therefore (X, Y, Z) pair can be anything like (3, 4, 5) / (4, 5, 6.4) and so on.
So, 2 can not answer the question independently.
Final answer : A



Manager
Joined: 27 Feb 2017
Posts: 123
Location: United States (WA)

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:27
My answer is (A). This is a relatively simple question.
In order to know the area of the right triangle, we just need to know the product of x and y.
From (a), we can tell 4xy = 80. That is sufficient. From (b), x = y + 1. There are indefinite number of possibilities. Not sufficient.
So, we should choose (A).



Manager
Joined: 27 May 2010
Posts: 199

What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
Updated on: 02 Jul 2019, 22:23
Think answer is A. Area = xy/2, so if we can find xy, we can determine the area. Statement 1: (X+y)^2  (xy)^2 = 80 x^2 + y^2 +2xy x^2  y^2 +2xy = 80 4xy = 80 => xy = 20 Therefore we can get value of xy and hence area. So statement 1 is sufficient. Statement 2: xy=1. We cannot determine xy using this. So statement 2 is not sufficient. So answer would be A. Posted from my mobile device
_________________
Please give Kudos if you like the post
Originally posted by prashanths on 02 Jul 2019, 08:28.
Last edited by prashanths on 02 Jul 2019, 22:23, edited 2 times in total.



Manager
Joined: 18 Sep 2018
Posts: 100

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:28
IMO A
By the image and sign of the angle, we can find it's a right triangle. So the area is 1/2*base*height = 1/2*y*x
St1: (x+y)^2−(x−y)^2=80 => 4xy = 80 [by simplifying (a+b)^2 and (ab)^2 formula) xy = 20, 1/2*x*y = 10 Sufficient
St2: (x−y)=1 => x=1+y => Area = 1/2*y*(1+y) => Not sufficient



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5304
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
Updated on: 03 Jul 2019, 08:06
#1 (X+y)^2  (xy)^2 = 80 x^2 + y^2 +2xy x^2  y^2 +2xy = 80 4xy = 80 => xy = 20 sufficient #2 (xy)=1 again x & y can be any integer value insufficient
IMO A What is the area of triangle ABC above, with side lengths x, y, and z?
(1) (x+y)2−(x−y)2=80(x+y)2−(x−y)2=80
(2) (x−y)=1
Originally posted by Archit3110 on 02 Jul 2019, 08:30.
Last edited by Archit3110 on 03 Jul 2019, 08:06, edited 1 time in total.



Senior Manager
Joined: 12 Dec 2015
Posts: 439

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:30
What is the area of triangle ABC above, with side lengths x, y, and z? means (1/2)xy =?
(1) (x+y)^2−(x−y)^2=80 ==> correct : 4xy = 80 => (1/2)xy =10
(2) (x−y)=1 ==> can't say (1/2)xy =? so the answer is A



VP
Joined: 20 Jul 2017
Posts: 1088
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
Show Tags
02 Jul 2019, 08:32
Area of triangle = 1/2*base*height = 1/2*y*x
(1) (x+y)^2−(x−y)^2=80 > x^2 + y^2 + 2xy  (x^2 + y^2  2xy) = 80 > x^2 + y^2 + 2xy  x^2  y^2 + 2xy = 80 > 4xy = 80 > xy = 20
Area = 1/2*xy = 1/2*20 = 10
Sufficient
(2) (x−y)=1 > x = y + 1
Area = 1/2*(y + 1)*y > Many values are possible
Insufficient
IMO Option A
Pls Hit Kudos if you like the solution




Re: What is the area of triangle ABC above, with side lengths x,y, and z?
[#permalink]
02 Jul 2019, 08:32



Go to page
1 2 3 4 5
Next
[ 93 posts ]



