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2 years ago

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A rectangle has a length of 32feet less than 8 times its width. If the area of the rectangle is 96 square feet, find the length

of the rectangle.

1 answer:

lesantik [10]2 years ago

5 0

L = 8w-32

w(8w-32) = 96

8x^2 - 32w - 96 = 0

w^2 - 4w - 12 = 0

(w - 6)(w + 2 ) = 0

w+2=0 results in negative measures

w-6=0 ---> w = 6

width is 6

length is 8(6) - 32 = 48-32 = 16

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So, in your case, we have

$\dfrac{\frac{2x}{3}-\frac{1}{2}}{\frac{3x}{4}-\frac{1}{2}} = \dfrac{\frac{4x-3}{6}}{\frac{3x-2}{4}} = \dfrac{4x-3}{6}\cdot \dfrac{4}{3x-2} = \dfrac{2(4x-3)}{3(3x-2)} = \dfrac{8x-6}{9x-6}$

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See answers and explanations below (along with a visual graph)

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