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Updated on: 27 Mar 2017, 06:36
Originally posted by BrentGMATPrepNow on 26 Mar 2017, 06:55.
Last edited by BrentGMATPrepNow on 27 Mar 2017, 06:36, edited 2 times in total.
Last edited by BrentGMATPrepNow on 27 Mar 2017, 06:36, edited 2 times in total.
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A
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Difficulty:
65%
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Question Stats:
63% (02:58) correct
37%
(03:03)
wrong
based on 330
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Right triangle ABC has sides with length x, y and z. If triangle ABC has perimeter 17, and x2 + y2 + z2 = 98, then what is the area of triangle ABC?
A) 12.75
B) 13.25
C) 14
D) 14.5
E) 15.25
* kudos for all correct solutions
EDIT: Changed perimeter to 17 (sorry)
A) 12.75
B) 13.25
C) 14
D) 14.5
E) 15.25
* kudos for all correct solutions
EDIT: Changed perimeter to 17 (sorry)
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27 Mar 2017, 06:35
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GMATPrepNow
Let z = length of hypotenuse
Let x and y = lengths of the sides that make up the triangle’s right angle
NOTE: since triangle area = (base)(height)/2, we know that the area of triangle ABC = [color=red]xy/2
Given: x² + y² + z² = 98
The Pythagorean Theorem tells us that x² + y² = z²
So, we can write: x² + y² + (x² + y²) = 98
Rewrite: 2(x² + y²) = 98
Or we can write: x² + y² = 49
Since we already know that x² + y² = z², we can conclude that z² = 49, which means z = 7
If the perimeter = 17, we can write: x + y + z = 17
Since z = 7, we can write: x + y + 7 = 17
Simplify to get: x + y = 10
IMPORTANT: If we square both sides of the above equation, some nice things happen.
(x + y) ² = 10²
Expand: x² + 2xy + y² = 100
Rearrange to get: (x² + y²) + 2xy = 100
Replace x² + y² with 49 to get: 49 + 2xy = 100
Simplify: 2xy = 51
NOTE: Our goal is to determine the value of xy/2
So, take 2xy = 51 and divide both sides by 4 to get: xy/2 = 51/4 = 12.75
Answer:
kavyagupta
Sure!!!
Please follow below attached fig.
As x^2+y^2=z^2----(1)
Also given x^2+y^2+z^2=98
putting value z^2 from (1)
2(x^2+y^2)= 98
or x^2+y^2=49------(2)
again putting x^2+y^2 =z^2 from (1)
z^2 =49 or z=7
Also given that perimeter x+y+z= 17
thus x+y= 17-7 =10---------(3)
sq both side to get
x^2+y^2+2xy =100
from (2)
2xy =100-49 =51
Also area = xy/2= 51/4 = 12.75
Ans 12.75
Ans A
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