Find the area of a rectangle if its diagonal is 15 cm in one of the sides 9 cm.

The diagonal of a rectangle splits this rectangle into two equal right-angled triangles.

Take triangle ABC, for example. Let’s pretend that:

AC = 15 cm;

BC = 9 cm.

Using the Pythagorean theorem, we calculate the length of the side AB:

AC ^ 2 = BC ^ 2 + AB ^ 2;

AB ^ 2 = AC ^ 2 – BC ^ 2;

AB ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144;

AB = √144 = 12 cm.

The area is equal to the product of length and width:

S = a b;

S = 12 * 9 = 108 cm2.

Answer: the area of the rectangle is 108 cm2.