Question

The length of a rectangle is 3 m more than its width. If its area is 180 m²; the length of the rectangle is ______.

Options

• 12 m

• 9 m

• 15 m

• 10 m

Answer 1

The length of a rectangle is 3 m more than its width. If its area is 180 m²; the length of the rectangle is 15 m.

Explanation:

Let the width of rectangle = x metre

∴ Length of rectangle = (x + 3) metre

Given area of rectangle = 180 m²

`\implies` x(x + 3) = 180

`\implies` x² + 3x – 180 = 0

`\implies` x² + 15x – 12x – 180 = 0

`\implies` x(x + 15) – 12(x + 15) = 0

`\implies` (x + 15)(x – 12) = 0

Either x + 15 = 0 or x – 12 = 0

`\implies` x = –15 or 12

But x > 0

∴ x = 12

Thus length of rectangle = x + 3

= (12 + 3) m

= 15 metre