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.
The perimeter of a rectangular garden is 80 feet, and the
This topic has expert replies
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 W = the width of the rectangleVJesus12 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 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 - L² = 391
Add L² to both sides: 40L = L² + 391
Subtract 40L from both sides: 0 = L² - 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
GMAT/MBA Expert
-
- Junior | Next Rank: 30 Posts
- Posts: 23
- Joined: Mon Mar 12, 2018 9:53 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.
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 GMAT® practice test or sample class
Ready to Prep? Exclusive discounts for Beat The GMAT® members HERE
GMAT Instructor and Master Trainer
Curious How You'll Score? Take a FREE GMAT® practice test or sample class
Ready to Prep? Exclusive discounts for Beat The GMAT® members HERE
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7294
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews