Question

In a rectangle the length is 2 cm longer than the width. If its length and width are both increase by 4 cm it's area is increased by 56 cm. Find the original length and width.

Answer 1

Length = 6 cm and width = 4 cm.

Explanation:

Let the width be x, then the length is x + 2 cm and its area = x(x + 2).

The new width and length are x + 4 and x + 6, and the new area is

(x + 4)(x + 6).

So we have the equation:-

(x + 6)(x + 4) = x(x + 2) + 56

x^2 + 10x + 24 = x^2 + 2x + 56

10x - 2x = 56 - 24

8x = 32

x = 4 cm = width

and length = 4 + 2 = 6 cm