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A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 1875 ft2.

User Nepa
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1 Answer

5 votes

Answer:

length = 75 ft and width = 25 ft

Explanation:

Let W = width of rectangle

Let L = length of rectangle

Area of a rectangle = L x W

Perimeter of a rectangle = 2L + 2W

Therefore, if the perimeter is 200 ft then:

2L + 2W = 200

2(L + W) = 200

L + W = 100

L = 100 - W

If the Area is 1875 ft² then: 1875 = L x W

Substitute the equation for L found above: 1875 = (100 - W) x W

Expand the brackets: 1875 = 100W - W²

Subtract 1875 from both sides: 100W - W² - 1875 = 0

Swap signs: W² - 100W + 1875 = 0

Factorize: (W - 25)(W - 75) = 0

Therefore, W = 25 or 75

If W = 25, then L = 100 - 25 = 75

If W = 75, then L = 100 - 75 = 25

Therefore, as length > width, length = 75 ft and width = 25 ft

User Jeniffer
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