One side of the rectangle is 3cm larger than the other side. find the area of the rectangle if the diagonal is 15 cm.

Let one side of the rectangle be x cm, then the other is (x + 3) cm.The adjacent sides of the rectangle and its diagonal form a right-angled triangle, for which, according to the Pythagorean theorem:

x ^ 2 + (x + 3) ^ 2 = 152;

x ^ 2 + x ^ 2 + 9 + 6x = 225;

2x ^ 2 + 6x + 9 – 225 = 0;

2x ^ 2 + 6x – 216 = 0;

x ^ 2 + 3x – 108 = 0.

D = 32 – 4 * (- 108) = 9 + 43 ^ 2 = 441 = 21 ^ 2.

x = (- 3 + √D) / 2 = (- 3 + 21) / 2 = 18/2 = 9 cm – one of the sides of the rectangle.

x + 3 = 9 + 3 = 12 cm – the second side of the rectangle.

The area of the rectangle is equal to the product of the sides:

S = 9 * 12 = 108 cm2.