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

So, L*W=A Because it is 4 cm longer, L=W+4 Because the area is 96, LW=96 Substitute to get W(W+4)=96 Multiply it out. W^2+4W-96=0 By solving the quadratic, W+12(W-8)=0 so either W+12 or W-8 is zero. The width must be positive, so the width is 8. Therefore the length is 12.

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adioabiola adioabiola · Answer 2 · 2021-10-21T12:07:20+02:00

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

Width of the envelope = x cm

Length of the envelope = (x + 4) cm

Area of the envelope = 96 square centimeters

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

find two numbers whose product is -96 and sum is +4

The two numbers are -12 and 8

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