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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

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

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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

Source: Beat The GMAT — Problem Solving | Tue Mar 03, 2020 6:42 am

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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