A rectangle with area 288 square inches has a length that is four less than four times the width. Find the length and the width of the rectangle.

Question

I am completely lost. I know that I must use substitution but that's it.

Answer 1

Let w be the width

then the length: "4 less than w" is represented as: 4w - 4

Since: A=L•W, then

288=w(4w - 4) use symmetric property to swap them if a=b then b=a

w(4w - 4) = 288 Distributive Property

4w² - 4w =288 subtract 288 from both sides

4w² - 4w - 288 = 0 divide every term by 4

w² - w - 72 = 0 Factor.

(w - 9)(w + 8) = 0 Zero product property if a•b=0 then a=0 or b=0

w= 9 or w= -8

w= 9 since the width cannot be negative

the length is 4(9)-4 --> 32

A= l•W

288= 32(9) check works!

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Answer 2

w represents the width

4w - 4 represents the length

w(4w - 4) = 288

4w² - 4w - 288 = 0

w² - w - 72 = 0

(w - 7)(w + 6) = 0

Can you solve for w and answer?