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

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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



OA C

Source: Veritas Prep

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BTGmoderatorDC wrote:
Thu May 06, 2021 3:36 pm
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



OA C

Source: Veritas Prep
\(\dfrac{1}{2} a^2 = 16\)

Side of triangle is \(4 \sqrt{2}\)

The ratio of sides of an isosceles triangle is \(1:1:\sqrt{2}.\)

Therefore, sides are in ratio of \(4\sqrt{2}: 4\sqrt{2}: 8.\)

Hence, larger side is \(8.\)

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BTGmoderatorDC wrote:
Thu May 06, 2021 3:36 pm
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



OA C

Source: Veritas Prep
Triangle XYZ is an isosceles right triangle.
Let's sketch an isosceles right triangle:
Image

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:
Image

This also means the last remaining vertex must be Z:
Image

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
Image

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.
Image

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
Image

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