SOLUTION: Monique wants to create a dog fence that has a perimeter of 112 feet. She knows that she wants the length to be 16 feet longer than the width.
Describe a method to calculate
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Question 743804: Monique wants to create a dog fence that has a perimeter of 112 feet. She knows that she wants the length to be 16 feet longer than the width.
Describe a method to calculate the length and the width of the fence.
Answer by davethejackal(28) (Show Source): You can put this solution on YOUR website!
Assuming the fence is rectangular in shape, then the total length of the perimeter is the length of all the sides = twice its length + twice its width
=2l + 2w
Where w = width of the fence, l = length (both measured in feet)
"a perimeter of 112 feet" so
2l + 2w = 112 | [1]
but "she wants the length to be 16 feet longer than the width" so
l = w +16 | [2]
Hence [1] becomes 2l + 2w = 2(w+16) + 2w = 4w + 32 = 112
Thus 4w = 112-32
And w = (112-32) / 4 = 80/4 = 20
[2] gives us l = w +16 = 20+16 = 36
Checking that the total length is 112 using [1]
2l+2w = 2(36)+2(20) = 72 + 40 = 112 QED
Hence the length of the fence is 32 ft and the width 20 ft.
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