Question

If the area of the rectangle below is 126 square meters, find the value of x.

Answer 1

x = 5

Explanation:

The area (A) o a rectangle is calculated as

A = lb ( l is length and b the breadth ), thus

x² + x - 12 ×
`(x+9)/(x-3)` = 126 ← factor the quadratic

(x + 4)(x - 3) ×
`(x+9)/(x-3)` = 126 ← cancel the common factor (x - 3)

(x + 4)(x + 9) = 126 ← expand factors using FOIL

x² + 13x + 36 = 126 ( subtract 126 from both sides )

x² + 13x - 90 = 0 ← in standard form

(x + 18)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 18 = 0 ⇒ x = - 18

x - 5 = 0 ⇒ x = 5

However x > 0 ⇒ x = 5