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

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The perimeter of a rectangular garden is 80 feet, and the area of the [#permalink]

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New post 21 Apr 2017, 00:05
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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

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Re: The perimeter of a rectangular garden is 80 feet, and the area of the [#permalink]

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New post 21 Apr 2017, 02:05
Perimeter of a rectangular garden is 80 feet ==> 2(L+B) = 80 ==> L+B= 40 feet

Area of the garden is 391 square feet ==> L*B = 391

From the options given, we can see that only 17 & 23 works out.

17+23 = 40
17 *23 = 391

Since 17 is the smallest, length of the shorter side of the garden = 17 feet.

Answer is A. 17 feet
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Re: The perimeter of a rectangular garden is 80 feet, and the area of the [#permalink]

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New post 21 Apr 2017, 10:28
391 is a weird number.

391 = area =
(some #)L * (some #)W

So I tried prime factorization of 391 first.

391 doesn't fit common divisibility rules, so start with prime 13.

391/13 is not an integer.

Try 391/17. Bingo: 17 x 23 = 391.

Check to see if 17 and 23 satisfy perimeter requirement.

2(17)=34. 2(23)=46. 34+46 = 80

So shorter side is 17. Answer: A

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Re: The perimeter of a rectangular garden is 80 feet, and the area of the [#permalink]

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New post 25 Apr 2017, 09:10
Bunuel 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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Re: The perimeter of a rectangular garden is 80 feet, and the area of the [#permalink]

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New post 25 Apr 2017, 13:01
You could even try process elimination for this. D & E can not be the answer as rectangle has 4 sides.
Let's look at A

If the perimeter was 80 then 80 - 34 = 46

The length of the longer side is 23

17 x 23 = 391

Therefore the answer is A
Re: The perimeter of a rectangular garden is 80 feet, and the area of the   [#permalink] 25 Apr 2017, 13:01
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