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

Triangle XYZ is an isosceles right triangle.
Let's sketch an isosceles right triangle:


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:


This also means the last remaining vertex must be Z:


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


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.


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

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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
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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

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.
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Refer diagram below:



We require to find hypotenuse XY of the triangle

Area \(= \frac{1}{2} a^2 = 16\)

a \(= 4\sqrt{2}\)

XY \(= \sqrt{(4\sqrt{2})^2 + (4\sqrt{2})^2} = \sqrt{64} = 8\)

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)
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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 )

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