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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If a rectangle of area \(24\) can be partitioned into exactly \(3\) nonoverlapping squares of equal area, what is the
This topic has expert replies
-
BTGmoderatorLU
- Moderator
- Posts: 2273
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's work backwardsBTGmoderatorLU wrote: ↑Fri May 19, 2023 11:08 amSource: 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
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
