An envelope is 4 cm longer than it is wide. the area is 96 square centimeters. find the length and width.

An envelope has the shape of a rectangle where the length is usually longer than the width.

The width of the envelope is 8 cm and the length of the envelope is 12 cm

Given:

let

Area of a rectangle = length × width

96 = (x + 4) × x

96 = x² + 4x

x² + 4x - 96 = 0

solve the quadratic equation using factorization method.

x² + 4x - 96 = 0

x² + 12x - 8x - 96 = 0

factorize

x(x + 12) - 8(x + 12) = 0

(x - 8) (x + 12) = 0

x - 8 = 0 or x + 12 = 0

x = 8 or x = -12

The width of the envelope can not be negative.

Therefore,

Width of the envelope = x cm

= 8 cm

Length of the envelope = (x + 4) cm

= (8 + 4)

= 12 cm

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