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If a rectangle of area \(24\) can be partitioned into exactly \(3\) nonoverlapping squares of equal area, what is the

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by BTGmoderatorLU » Fri May 19, 2023 11:08 am

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Source: Official Guide

If a rectangle of area \(24\) can be partitioned into exactly \(3\) nonoverlapping squares of equal area, what is the length of the longest side of the rectangle?

A. \(2\sqrt{2}\)
B. \(6\)
C. \(8\)
D. \(6\sqrt{2}\)
E. \(12\sqrt{2}\)

The OA is D
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Re: If a rectangle of area \(24\) can be partitioned into exactly \(3\) nonoverlapping squares of equal area, what is th

by Brent@GMATPrepNow » Sat May 27, 2023 5:22 am
BTGmoderatorLU wrote: ↑
Fri May 19, 2023 11:08 am
 Source: Official Guide

If a rectangle of area \(24\) can be partitioned into exactly \(3\) nonoverlapping squares of equal area, what is the length of the longest side of the rectangle?

A. \(2\sqrt{2}\)
B. \(6\)
C. \(8\)
D. \(6\sqrt{2}\)
E. \(12\sqrt{2}\)

The OA is D
Let's work backwards

Here are 3 squares (with sides length x) comprising a rectangle
Image

So, the rectangle has base of 3x and height of x
Image

GIVEN: The rectangle has area 24
Area of rectangle = (base)(height)

We can write: 24 = (3x)(x)
Simplify: 24 = 3x²
So 8 = x²
This means x = √8 = √[(4)(2)] = (√4)(√2) = 2√2

What is the length of the longest side of the rectangle?
The longest side had length 3x
3x = 3(2√2) = 6√2

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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