Question

The area of a rectangle is x² + 7x + 12. If its breadth is (x + 3), then find its length.

Answer 1

Let the length of the rectangle be l.

Given, area of a rectangle = x² + 7x + 12

And breadth = x + 3

We know that,

Area of rectangle = Length × Breadth

⇒ x² + 7x + 12 = l × (x + 3)

⇒ `l = (x^2 + 7x + 12)/(x + 3)`

= `(x^2 + 4x + 3x + 12)/(x + 3)`

= `(x(x + 4) + 3(x + 4))/(x + 3)`

= `((x + 4)(x + 3))/(x + 3)`

= x + 4

Hence, the length of rectangle = x + 4