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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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu May 06, 2021 3:36 pm

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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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Source: Beat The GMAT — Problem Solving | Thu May 06, 2021 3:36 pm

swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Fri May 07, 2021 10:53 am

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

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

by Brent@GMATPrepNow » Sat May 08, 2021 8:48 am

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:

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

Brent Hanneson - Creator of GMATPrepNow.com

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