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the length of a rectangular flower bed is 7 feet less than 3 times its width. the area of the bed is 20 feet squared. find the dimensions of the flower bed.

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2 Answers

Let x = width, and thus the length = 3x-7

Area = x(3x-7) = 20

Solve for x ,

x = 4 ft

3x-7 = 5 ft

Answer: 4 ft x 5 ft

 

Let W be the width in feet. Translating the first sentence we see that the length is L = 3W - 7.

The area is given by A=LW so we get:

(3W - 7)W = 20

3W2 - 7W - 20 = 0

(3W + 5)(W - 4) = 0

W = -5/3 or W = 4.

However, the width can't be negative. Thus W = 4 and L = A/W = 20/4 = 5.

we can double-check that this works: 3*4 - 7 = 12 - 7 = 5.

So it is a 5 ft. x 4 ft. (L x W) flower bed.