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

1. 12 m

2. 9 m

3. 15 m

4. 10 m

Let width be x meters and length be (x + 3) meters.

Given,

Area = 180 m²

⇒ x(x + 3) = 180

⇒ x² + 3x = 180

⇒ x² + 3x - 180 = 0

⇒ x² + 15x - 12x - 180 = 0

⇒ x(x + 15) - 12(x + 15) = 0

⇒ (x - 12)(x + 15) = 0

⇒ x - 12 = 0 or x + 15 = 0

⇒ x = 12 or x = -15.

Since, width cannot be negative.

∴ x = 12 meters.

Length = x + 3 = 12 + 3 = 15 meters.

Hence, Option 3 is the correct option.