Carcass wrote:
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 the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math Book Triangle XYZ is an isosceles right triangle. Let's sketch an isosceles right triangle:
Side XY is longer than side YZSince 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
jArea of triangle = (base)(height)/2So, 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