Question

The area of a rectangle is 70 square inches. The length is x – 2, and the width is x + 1. Find the value of x, and the dimensions of the rectangle. A=lw x =

Answer 1

x = 9

Length = 7

Width = 10

Explanation:

Given that :

Length = x - 2

Width = x + 1

Area = 70in²

Area of rectangle

(x - 2) * (x + 1)

x² + x - 2x - 2 = 70

X² - x - 2 = 70

x² - x - 2 - 70

x² - x - 72 = 0

x² - 9x + 8x - 72 = 0

Factorize

x(x - 9) +8(x - 9) = 0

(x - 9) = 0 or (x + 8) = 0

x = 9 or x = - 8

x cannot be negative ; Hence, x = 9

Length = x - 2 = 9 - 2 = 7

Width = x + 1 = 9 + 1 = 10