In the rectangle, the diagonal is 13 and the larger side is 12. Find the smaller side of the rectangle.

A rectangle is a quadrangle in which all angles are right and equal to each other.

In order to find the length of the shorter side AB, consider the triangle ΔABS. This triangle is rectangular.

To calculate, we use the Pythagorean theorem, according to which, the square of the hypotenuse is equal to the sum of the squares of the legs:

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

AB ^ 2 = AC ^ 2 – BC ^ 2;

AB ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25;

AB = √25 = 5 cm.

Answer: The length of the smaller side of the rectangle is 5 cm.