In description

Question

A builder wants to create a rectangular room in a house. She wants it to have a total area of 375 square feet, and it should be 10 feet longer than it is wide. What dimensions should she use for the room? Round to the nearest tenth of a foot, if necessary.

Answer 1

For any rectangle, Area = Length x width

 

Here, let length = x, let width = (x - 10), since it is 10 ft longer than wide. 

 

Area = L  •   W

 

375 = x(x - 5)

375 = x^2 - 5x

0 = x^2 - 5x - 375

0 = (x + 15)(x - 25)

x + 15 = 0       x- 25 = 0

x = -15            x = 25

 

Therefore, x = 25, since we reject negative values for distances. 

 

x = length = 25 ft

(x - 10) = 25 - 10 = width = 15 ft

 

As a check: 25 • 15 = 375