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If a rectangle of area 24 can be partitioned into exactly 3

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by BTGModeratorVI » Tue Mar 03, 2020 6:42 am

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Answers

A

B

C

D

E

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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√2
B. 6
C. 8
D. 6√2
E. 12√2

Answer: D
Source: Official Guide
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Re: If a rectangle of area 24 can be partitioned into exactly 3

by swerve » Tue Mar 03, 2020 10:02 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:42 am
 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√2
B. 6
C. 8
D. 6√2
E. 12√2

Answer: D
Source: Official Guide
Area of rectangle: \(L\cdot W = 24\)

Since the areas of the 3 squares are equal, we can divide by 3 to get the area of 1 square.
\(\dfrac{L\cdot W}{3} = 8\)
side\(^2 = 8\)
side \(= 2\sqrt{2}\)

This is trap answer A

B, C are also out because the side length won't be an integer, so D, E are left.

The side of the square is the shorter side of the rectangle, to find the other side multiply \(2\sqrt{2} \cdot 3 = 6\sqrt{2}\)
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Re: If a rectangle of area 24 can be partitioned into exactly 3

by Brent@GMATPrepNow » Tue Mar 03, 2020 10:29 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:42 am
 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√2
B. 6
C. 8
D. 6√2
E. 12√2

Answer: D
Source: Official Guide
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

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Brent
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Re: If a rectangle of area 24 can be partitioned into exactly 3

by Scott@TargetTestPrep » Wed Mar 11, 2020 9:38 am
BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:42 am
 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√2
B. 6
C. 8
D. 6√2
E. 12√2

Answer: D
Source: Official Guide
Since the 3 non overlapping squares have equal area, the area of each square is 24/3 = 8, and thus the side of each square is √8. Therefore, the rectangle’s width is √8, and its length is 3 times the width, or 3√8 = 3(2√2) = 6√2.

Answer: D

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