The length of the rectangle is 2cm longer than the width. Find the diagonal of this rectangle if its area is 24cm ^ 2.

We denote the width by x cm, then the length of the rectangle is x + 2 cm, and the area is x * (x + 2) cm2.

Let’s make an equation for the area.

x * (x + 2) = 24.

x ^ 2 + 2x – 24 = 0.

D = 2 * 2 + 4 * 24 = 4 + 96 = 100 = 10 ^ 2.

x = (- 2 + 10) / 2 = 4 cm – width.

4 + 2 = 6 cm – length.

Find the diagonal of the rectangle using the Pythagorean theorem.

d = √ (6 ^ 2 + 4 ^ 2) = √52 = 2√13 cm.

Answer: the diagonal of the rectangle is 2√13 centimeters.