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3 years ago

The perimeter of a rectangular garden is 110ft. The length is 5 ft greater than the width. Find the length and width.

Mathematics

1 answer:

tigry1 [53]3 years ago

4 0

P = perimeter

L = length

W = width

Formula for the perimeter of a rectangle = L + L + W + W or P = 2L + 2W

You know:

P = 110ft

L = W + 5 [length is 5ft greater than the width]

So plug this into the formula:

P = 2L + 2W Substitute/plug in (W + 5) for L

110 = 2(W + 5) + 2W Distribute/multiply 2 into (W + 5)

110 = (2)W + (2)5 + 2W

110 = 2W + 10 + 2W Combine like terms (2W + 2W)

110 = 4W + 10 Subtract 10 on both sides

110 - 10 = 4W + 10 - 10

100 = 4W Divide 4 on both sides to get "W" by itself

$\frac{100}{4}=\frac{4W}{4}$

25 = W Now that you know the width, plug it into the equation for length

L = W + 5 Plug in 25 for W

L = 25 + 5

L = 30

L = 30 ft

W = 25 ft

PROOF

P = 2L + 2W

110 = 2(30) + 2(25)

110 = 60 + 50

110 = 110

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