Rectangle word problem

The length of a rectangle is 5 more than the width and the area is 24. Find the length and the width.

Solution

The formula of the area of a rectangle is

A = L * w

Translate the phrase "The length of a rectangle is 5 more than the width" into an equation.

We get: L = w + 5

Replace A by 24 and replace L by w + 5

24 = (w + 5) * w

24 = w² + 5w

24 - 24 = w² + 5w - 24

0 = w² + 5w - 24

Factor the expression on the right

0 = ( w + blank) * ( w + blank)


To get blank, look for factors of -24 that will add up to 5.

8 * -3 = -24 and 8 + -3 = 5

So fill in the blank with 8 and -3

0 = (w + 8) * ( w + -3)

Now solve the above

w + 8 = 0

w + -3 = 0


w + 8 = 0

w + 8 - 8 = 0- 8

w = -8. The answer cannot be negative

w + -3 = 0

w + -3 + 3 = 0 + 3

w = 3

L = w + 5 = 3 + 5 = 8