It is currently 19 Feb 2018, 02:23

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Current Student
avatar
Joined: 17 Jul 2013
Posts: 48
GMAT 1: 710 Q49 V38
GRE 1: 326 Q166 V160
GPA: 3.74
XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 31 Oct 2014, 06:43
3
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:18) correct 42% (01:40) wrong based on 153 sessions

HideShow timer Statistics

XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the hypotenuse. A circle with center O and radius x has been inscribed in the triangle. What is the value of x?

A) 1.8
B) 2
C) 2.4
D) 3
E) 4
[Reveal] Spoiler: OA
2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 278
Premium Member
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 31 Oct 2014, 12:15
2
This post received
KUDOS
1
This post was
BOOKMARKED
megatron13 wrote:
XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the hypotenuse. A circle with center O and radius x has been inscribed in the triangle. What is the value of x?

A) 1.8
B) 2
C) 2.4
D) 3
E) 4

Attachments

File comment: solution
finalsol.jpg
finalsol.jpg [ 41.76 KiB | Viewed 10701 times ]

11 KUDOS received
Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 206
GMAT ToolKit User
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 31 Oct 2014, 21:27
11
This post received
KUDOS
6
This post was
BOOKMARKED
megatron13 wrote:
XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the hypotenuse. A circle with center O and radius x has been inscribed in the triangle. What is the value of x?

A) 1.8
B) 2
C) 2.4
D) 3
E) 4


Draw the triangle, connect OX, OY, OZ
Hypotenuse = 10
Area of XYZ = 8*6/2 = 24
Area of OXZ = x*10/2 = 5x
Area of OXY = x*8/2 = 4x
Area of OYZ = x*6/2 = 3x
Area of OXZ + Area of OXY + Area of OYZ = Area of XYZ -> 5x + 4x + 3x = 24 ---> x = 2
_________________

.........................................................................
+1 Kudos please, if you like my post

1 KUDOS received
Intern
Intern
avatar
Joined: 19 Jul 2013
Posts: 44
GMAT ToolKit User
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 31 Oct 2014, 22:00
1
This post received
KUDOS
megatron13 wrote:
XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the hypotenuse. A circle with center O and radius x has been inscribed in the triangle. What is the value of x?

A) 1.8
B) 2
C) 2.4
D) 3
E) 4


Easier solution.
Draw the diagram. Let the circle touch XY at P, YZ at Q and XZ at R. Then PY = YQ = radius of the circle(x). Now remember all the sides of the triangle are like tangents to the circle and both tangents from any external point to a circle are equal in size. So XP = XR and RZ = QZ. Also XP = 8-x and QZ = 6-x. So (8-x)+(6-x)=XP+QZ=XR+RZ=XZ=10. So x=2.
Manager
Manager
avatar
B
Status: single
Joined: 19 Jan 2015
Posts: 95
Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)
Premium Member
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 07 Mar 2015, 04:52
area of triangle =1/2bh

Another formula is , r s , r= inradius of triangle and s= semiperimeter of triangle.
here sides 6,8and 10.
area of triangle =1/2 *6*8=24
semiperimeter ,s=>12
rs=24=> r *12=24
r=2.
Option B is sufficient.

Here some lists of area of triangles formula.
A=1/2bh

A=1/2ab sinC, a and b are two sides , both included angle SinC

A=abc /4R ,=> R= circumradius of triangle.

A=rs , r is inradius of triangle, s is semiperimeter of triangle
2 KUDOS received
Intern
Intern
User avatar
Joined: 12 Jul 2015
Posts: 27
Location: United States
Concentration: Strategy, General Management
WE: General Management (Pharmaceuticals and Biotech)
GMAT ToolKit User
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 20 Dec 2015, 04:59
2
This post received
KUDOS
2
This post was
BOOKMARKED
The 3 sides of a right angle triangle = 6,8,10

Radius of a circle inscribed in the right triangle r = (a+b-c)/2 where c is the hyp and a and b are other two sides.

On substituting: (6+8-10)/2
r = 2

Its a time saver!
Intern
Intern
avatar
Joined: 30 Nov 2015
Posts: 9
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 23 Dec 2015, 15:24
dayavenket wrote:
The 3 sides of a right angle triangle = 6,8,10

Radius of a circle inscribed in the right triangle r = (a+b-c)/2 where c is the hyp and a and b are other two sides.

On substituting: (6+8-10)/2
r = 2

Its a time saver!


is this a legit formula?
2 KUDOS received
Intern
Intern
User avatar
Joined: 12 Jul 2015
Posts: 27
Location: United States
Concentration: Strategy, General Management
WE: General Management (Pharmaceuticals and Biotech)
GMAT ToolKit User
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 24 Dec 2015, 05:15
2
This post received
KUDOS
1
This post was
BOOKMARKED
daisuke123 wrote:
dayavenket wrote:
The 3 sides of a right angle triangle = 6,8,10

Radius of a circle inscribed in the right triangle r = (a+b-c)/2 where c is the hyp and a and b are other two sides.

On substituting: (6+8-10)/2
r = 2

Its a time saver!


is this a legit formula?



Yes, You can derive this equation easily. Find enclosed the picture.

If r be the radius of the inscribed circle, then the red length on the vertical edge is given by a−r; similarly the blue length on the horizontal edge is given by b−r.

Using the property that tangential distances are equal we get a−r+b−r=c.

=> a+b−2r = c or r=(a+b−c)/2

Hope this helps! :)
Attachments

File comment: Right triangle
right triangle.png
right triangle.png [ 9.57 KiB | Viewed 8514 times ]

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13827
Premium Member
Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h [#permalink]

Show Tags

New post 05 Mar 2017, 05:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h   [#permalink] 05 Mar 2017, 05:42
Display posts from previous: Sort by

XYZ is a right angled triangle with YZ = 6cm and XY = 8cm. XZ is the h

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.