## If a rectangle of area $$24$$ can be partitioned into exactly $$3$$ nonoverlapping squares of equal area, what is the

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### If a rectangle of area $$24$$ can be partitioned into exactly $$3$$ nonoverlapping squares of equal area, what is the

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

00:00

A

B

C

D

E

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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

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

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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