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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

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

by BTGModeratorVI » Sun Sep 27, 2020 7:00 am

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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

Answer: C
Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sun Sep 27, 2020 7:00 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: Triangle XYZ is an isosceles right triangle. If side XY is

by Brent@GMATPrepNow » Sat Oct 03, 2020 6:20 am

BTGModeratorVI wrote: ↑
Sun Sep 27, 2020 7:00 am
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

Answer: C
Source: Veritas Prep

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.