Question

A rectangle with an area of 104 square inches has a width that is 5 inches less than it's length.

Part A

Write an equation representing the area of the rectangle. Use x to represent the length of the rectangle.

Solve your equation for all values of x.

Answer 1

The equation of the area is ⇒ x(x - 5) = 104

The values of x = 13 and -8

Explanation:

∵ The length of the rectangle = x

∴ The width of the rectangle = x - 5

∵ The area of the rectangle = length × width

∴ x(x - 5) = 104 ⇒ the equation representing the area of the rectangle

We will solve the equation to find the values of x

∴
`x^(2)-5x=104`

∴
`x^(2)-5x-104=0`⇒ factorize the quadratic equation

∴ (x - 13)(x + 8) = 0

∴ x - 13 = 0 and x + 8 = 0

∴ x = 13

∴ x = -8 ⇒ we can not use this because there is no length with -ve value

∴ The length of the rectangle is 13 inches and the width is 8 inches