The perimeter of a rectangular garden is 80 feet, and the

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

The perimeter of a rectangular garden is 80 feet, and the

by VJesus12 » Fri May 11, 2018 7:19 am

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The perimeter of a rectangular garden is 80 feet, and the area of the garden is 391 square feet. What is the length of the shorter side of the garden?

A. 17 feet
B. 23 feet
C. 34 feet
D. 40 feet
E. 46 feet

The OA is the option A.

How can I find the dimensions of the garden? What are the equations that help me here? I need some help. Please.

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Source: Beat The GMAT — Problem Solving | Fri May 11, 2018 7:19 am

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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

by Brent@GMATPrepNow » Fri May 11, 2018 7:34 am

VJesus12 wrote:The perimeter of a rectangular garden is 80 feet, and the area of the garden is 391 square feet. What is the length of the shorter side of the garden?

A. 17 feet
B. 23 feet
C. 34 feet
D. 40 feet
E. 46 feet

Let W = the width of the rectangle
Let L = the length of the rectangle

The perimeter of a rectangular garden is 80 feet
We can write: W + W + L + L = 80
Simplify to get: 2W + 2L = 80
Divide both sides by 2 to get: W + L = 40

The area of the garden is 391 square feet
Area = (length)(width)
We can write: LW = 391

We now have two equations:
W + L = 40
LW = 391

Rewrite W + L = 40 to get: W = 40 - L
Now, take LW = 391 and replace W with 40 - L to get: L(40 - L) = 391
Expand: 40L - LÂ² = 391
Add LÂ² to both sides: 40L = LÂ² + 391
Subtract 40L from both sides: 0 = LÂ² - 40L + 391
Factor the right side: 0 = (L - 17)(L - 23)

So, L = 17 or L = 23
If L = 17, then W = 23 (since we know that W + L = 40)
If L = 23, then W = 17
So, the rectangle's two dimensions are 17 and 23

What is the length of the shorter side of the garden?
The shorter side has length 17

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jake@ThePrincetonReview: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Mon Mar 12, 2018 9:53 am

by Jake@ThePrincetonReview » Fri May 11, 2018 11:12 am

Alternatively, you could just use the answer choices to solve this problem. Let's start in the middle, with answer choice C: If the "shorter" side is 34 feet, the "longer" side would have to be 6 feet in order to make the perimeter equal to 80 [(2 x longer side) + (2 x shorter side) = 80, so longer side + shorter side = 40.] . Clearly, that doesn't work. The "shorter" side would have be much smaller. Answer choice B is also too large because the shorter side being 23 would make the "longer" side 17. The only answer that seems reasonable is answer choice A. Short side = 17, Long side therefore =23. And 17 x 23 is indeed 391. All done.
Often, using real numbers is easier than algebra. So if you feel like you want to use algebra to solve a problem, and there are integers in the answer choices, tell yourself that one of those answers has to be the right one, so testing them out will get you the answer with less stress.

Jake Schiff
GMAT Instructor and Master Trainer

Curious How You'll Score? Take a FREE GMATÂ® practice test or sample class
Ready to Prep? Exclusive discounts for Beat The GMATÂ® members HERE

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue May 07, 2019 5:40 pm

VJesus12 wrote:The perimeter of a rectangular garden is 80 feet, and the area of the garden is 391 square feet. What is the length of the shorter side of the garden?

A. 17 feet
B. 23 feet
C. 34 feet
D. 40 feet
E. 46 feet

Since perimeter = 2L + 2W, and area = WL, we can create the following two equations:

2L + 2W = 80

L + W = 40

L = 40 - W

WL = 391

We can substitute 40 - W for L in the equation WL = 391:

W(40 - W) = 391

40W - W^2 = 391

W^2 - 40W + 391 = 0

(W - 17)(W - 23) = 0

W = 17 or W = 23

Thus we see that the shorter side of the rectangle is 17.

Alternate Solution:

Since perimeter = 2L + 2W:

2L + 2W = 80

L + W = 40

Since this is the sum of the shorter and longer sides of the rectangle, the shorter side must be less than 20 (if the shorter side is greater than 20 and the longer side is even longer, they would add up to a value greater than 40). The only answer choice that is less than 20 is A.

Answer: A

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