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I am a rectangle, and my area is 80 square inches. My width is 2 inches shorter than my length. What is my perimeter?

Respuesta :

akaleti47
area=l*b=l*(l-2)=80(given)

so, l^2 - 2l =80
   l^2 - 2l - 80=0
   l=10 or -8

l=10,b=10-2=8
perimeter=2(l+b)=2(18)=36

The perimeter of the rectangle is 36 inches.

Area of rectangle:

  • area = lw

where

l = length

w = width

area = 80 inches²

The width is 2 inches shorter than my length. Therefore,

  • l = w + 2

80 = w(w + 2)

80 = w² + 2w

w² + 2w - 80 = 0

w² - 8w + 10w - 80 = 0

w(w - 8) + 10(w - 8) = 0

(w + 10)(w - 8) = 0

w = -10

w = 8

The width can only be positive. Therefore, w = 8 inches.

perimeter of a rectangle :

  • perimeter = 2(l + w) = 2(10 + 8) = 36 inches

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