Triangle XYZ is an isosceles right triangle. If side XY is longer than

Question

Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 16, what is the measure of side XY?

A. 4
B. 4√2
C. 8
D. 8√2
E. Cannot be determined from the information provided

Kudos for a correct  solution .

BrentGMATPrepNow · Accepted Answer

Triangle XYZ is an isosceles right triangle.   
Let's sketch an isosceles right triangle: 
 https://i.imgur.com/N3UOppf.png

Side XY is longer than side YZ  
Since the hypotenuse is the longest side of a right triangle, side XY must be the hypotenuse. Add this to our diagram: 
 https://i.imgur.com/SxksdIu.png

This also means the last remaining vertex must be Z:
 https://i.imgur.com/uY8j7uo.png

The area of the triangle is 16. What is the measure of side XY?  
Let  j  = the length of side ZY, 
Since ZY = ZX, we can see that side ZX must also halve length  j 
 https://i.imgur.com/b0JMqYb.png

Area of triangle = (base)(height)/2 
So, we can write: 16 = ( j )( j )/2
Simplify: 16 = j²/2
Multiply both sides by 2 to get: 32 = j²
Solve:  j = √32

What is the measure of side XY?  
Our diagram now looks like this.
 https://i.imgur.com/Tnij4d2.png

Applying the Pythagorean Theorem, we can write: (√32)² + (√32)² = c²
Simplify: 32 + 32 = c²
Simplify: 64 = c²
Solve: c = 8

Answer: C

Cheers, 
Brent

RELATED VIDEO 
 https://www.youtube.com/watch?v=iUUP2sp4ogg

chetan2u · Answer

ans C ..8..
 xy being larger means it is the hyp..
 area =(1/2)*(yz)^2=16 or yz=4*\sqrt{2}..
 therefore hyp=xy=8

arunrnair · Answer

1/2 a^2 = 16 
Side of triangle is 4 root 2 
The ratio of sides of an isoceles triangle is 1:1:root 2. 
There fore sides are in ratio of 4 root 2: 4 root 2: 8.
larger side is 8

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

While the stimulus doesn't seem to contain a ton of information, the terms "isosceles" and "right" that define the triangle make that one value (Area = 16) go a long way. Since you know that XY is longer than YZ, then XY must be the hypotenuse and sides YZ and XZ must be the shorter sides. Meaning, also that side XY will be equal to side YZ√2.

With an isosceles right triangle, you also know that the area (which here is 16) is equal to 1/2*(shorterside)^2. So that means that here 16=1/2*s^2 and that one of the shorter sides then measures 4√2. Since the hypotenuse, then is s√2, you'll multiply 4√2(√2) to find that side XY measures 8.

PareshGmat · Answer

Refer diagram below: tri.png We require to find hypotenuse XY of the triangle Area = \frac{1}{2} a^2 = 16 a = 4\sqrt{2} XY = \sqrt{(4\sqrt{2})^2 + (4\sqrt{2})^2} = \sqrt{64} = 8

KarishmaB · Answer

In an isosceles right triangle, the two legs are equal in length and the hypotenuse is sqrt(2) times the length of the legs. If the side XY is longer than side YZ, XY must be the hypotenuse.

Area of isosceles right triangle  = (1/2)*side^2 = 16 
 Side = 4\sqrt{2}

Hypotenuse  XY = \sqrt{2}*4\sqrt{2} = 8

Answer (C)

kumarankit01 · Answer

According to the give condition , XY is hypotenuse

So we have ,

1\2 *XZ*YZ=16

XZ^2 = 32 ( XZ=YZ , Isosceles Triangle)

XZ = 4*2^1/2

So XY = 8 ( apply Pythagoras Theorem )

bumpbot · Answer

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Triangle XYZ is an isosceles right triangle. If side XY is longer than

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Triangle XYZ is an isosceles right triangle. If side XY is longer than

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