SOLUTION: The length of a rectangle is 4 cm less than twice it's width. Find the length and the width given the area is 70 cm^2.

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Question 848222: The length of a rectangle is 4 cm less than twice it's width. Find the length and the width given the area is 70 cm^2.
Answer by jim_thompson5910(35256) About Me  (Show Source):
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The length of a rectangle is 4 cm less than twice it's width. Find the length and the width given the area is 70 cm^2.

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Let x = width

"The length of a rectangle is 4 cm less than twice it's width" ----> Length = 2x - 4


Area = Length * Width

70 = (2x-4) * x

70 = x(2x-4)

70 = 2x^2-4x

0 = 2x^2-4x - 70

2x^2 - 4x - 70 = 0

2(x^2 - 2x - 35) = 0

x^2 - 2x - 35 = 0/2

x^2 - 2x - 35 = 0

(x - 7)(x + 5) = 0

x - 7 = 0 or x + 5 = 0

x = 7 or x = -5

Toss the negative result. You can't have a negative width.

The width is 7 cm

Width = x = 7

Length = 2x - 4

Length = 2(7) - 4 ... plug in x = 7

Length = 14 - 4

Length = 10

The length is 10 cm