Question

Mayrin has rectangular rug with an area of 36 square feet. The area is represented by the equation f(x)= x2 + 5x – 36 and this rug is 5 feet longer than it is wide. What are the dimensions of the rug?

Answer 1

B) width = 4 ft

length = 9 ft

Explanation:

Area = 36 ft²

Let width = x

⇒ length = x + 5

Area of a rectangle = width × length

⇒ 36 = x(x + 5)

⇒ x² + 5x - 36 = 0

⇒ x² + 9x - 4x - 36 = 0

⇒ (x² + 9x) + (-4x - 36) = 0

⇒ x(x + 9) - 4(x + 9) = 0

⇒ (x + 9)(x - 4) = 0

⇒ x = -9, x = 4

As distance is positive, x = 4 only

Therefore,

width = x = 4 ft

length = x + 5 = 4 + 5 = 9 ft