In a rhombus, the lengths of the diagonals are 16 cm and 12 cm. What is the…

Concept

The diagonals of a rhombus bisect each other at right angles.

Therefore, a side of the rhombus is the hypotenuse of a right triangle whose legs are half the two diagonals; the Pythagorean theorem determines its length.

Application

1. Half of the 16 cm diagonal is 16 ÷ 2 = 8 cm.

2. Half of the 12 cm diagonal is 12 ÷ 2 = 6 cm.

3. Let the side length be s. Then s2 = 82 + 62 = 64 + 36 = 100.

4. Taking the positive square root, s = √100 = 10 cm.

Cross-check

The half-diagonals form a 6-8-10 right triangle, which is twice the 3-4-5 Pythagorean triple.

Hence, the side of the rhombus is 10 cm.