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# If a rectangular billboard has an area of 104 square feet and a perime

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Math Expert
Joined: 02 Sep 2009
Posts: 60496
If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

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27 Dec 2015, 10:47
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Difficulty:

25% (medium)

Question Stats:

78% (02:02) correct 22% (02:18) wrong based on 95 sessions

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If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

A. 4
B. 7
C. 8
D. 13
E. 26

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Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

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28 Dec 2015, 23:02
1
Hi All,

This question can be solved algebraically or by TESTing THE ANSWERS.

We're told that a rectangle has an area of 104 and a perimeter of 42. We're asked for the length of one of the SHORTER sides of the rectangle.

Since the answers are all INTEGERS, and the area is 104, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 104, so the correct answer is probably A or C.

IF...
The shorter side = 8...
The area = 104....104/8 = 13 = the longer side
Perimeter = 8+8+13+13 = 42
This is an exact MATCH for what we were told, so this MUST be the answer.

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Rich
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Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

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27 Dec 2015, 21:55
If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

l*w=104

2l+2w=42
l+w=21
l=21-w

(21-w)*w=104
solve for w.
w = 8 or 13

shorter side = 8

C. 8
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Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

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29 Dec 2015, 02:45
Bunuel wrote:
If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

A. 4
B. 7
C. 8
D. 13
E. 26

Assume the sides to be x and y.

Perimeter = 2x + 2y = 42
Hence x + y = 21 - (i)

Area = xy = 104 - (ii)

Since these are the sides of a billboard, we are dealing with positive numbers only and the options tell us that they are integers.
104 can be written as a product of two numbers as 104*1 or 52*2 or 26*4 or 13*8

Of these, only 13*8 satisfies the equation (i)
Hence the lengths are 13 and 8

Length of shorter side = 8
Option C
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Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

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14 Sep 2018, 17:37
Bunuel wrote:
If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

A. 4
B. 7
C. 8
D. 13
E. 26

We can create the following equations:

LW = 104

and

2L + 2W = 42

L + W = 21

W = 21 - L

Substituting, we have:

L(21 - L) = 104

21L - L^2 = 104

L^2 - 21L + 104 = 0

(L - 13)(L - 8) = 0

L = 13 or L = 8

Thus, the shorter side is 8.

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Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

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30 Nov 2019, 13:07
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Re: If a rectangular billboard has an area of 104 square feet and a perime   [#permalink] 30 Nov 2019, 13:07
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