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The area of a bulletin board is 90 ft. The length is nine feet less than four times the width. Find the length and the width, in feet, of the bulletin board.
width
ft
length
ft
+

Respuesta :

Area (A) = 90 ft
Width = x
Length = 4x - 9

A = L*W, so the equation is:
x(4x - 9) = 90

Solve:
4x^2 - 9x = 90
4x^2 - 9x - 90 = 0
(4x + 15)(x - 6) = 0
4x + 15 = 0
4x = - 15
x = -15/4
^^^ reject because distance can’t be negative
x - 6 = 0
x = 6 ft (width)

Length = 4x - 9
L = 4(6) - 9
L = 24 - 9
L = 15 ft

Check:
A = L*W
90 = 15 * 6
90 = 90

Answer: The length is 15 feet and the width is 6 feet.

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