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)

⇒ ${\displaystyle l=\frac{x^2+7x+12}{x+3}}$

= ${\displaystyle \frac{x^2+4x+3x+12}{x+3}}$

= ${\displaystyle \frac{x(x+4)+3(x+4)}{x+3}}$

= ${\displaystyle \frac{(x+4)(x+3)}{x+3}}$

= x + 4

Hence, the length of rectangle = x + 4