A flag for a local organization is in the shape of a rectangle whose length is 4 inches less than twice its width. If the area of the flag is 30 square inches,

Question

A flag for a local organization is in the shape of a rectangle whose length is 4 inches less than twice its width. If the area of the flag is 30 square inches, find its dimensions (length and width).

Answer 1

A = lw

l = 2w - 4

 

(2w - 4)w = 30

2w² - 4w - 30 = 0

w² - 2w - 15 = 0

(w - 5)(w + 3) = 0

 

For the left side to equal 0, one of the factors has to equal 0.

 

w - 5 = 0

w = 5

l = 2(5) - 4

l = 6

 

w + 3 = 0

w = -3

We don't measure in negative numbers, so we distegard this answer.

Answer 2

Let w = the width

Let 2w - 4 = the length

A = lw

w(2w - 4) = 30

2w² - 4w - 30 = 0       Divide both sides by 2.

w² - 2w - 15 = 0

(w - 5)(w + 3) = 0

w - 5 = 0    or    w + 3 = 0

w = 5 inches     w = -3, illogical answer

2w - 4 = 2(5) - 4 = 6 inches