The diagonals of a rhombus are 16 cm and 12 cm find the length of the side.

Analyze the question: We are given a rhombus with diagonals 16 cm and 12 cm, and we need the length of its side.

Concept: The diagonals of a rhombus bisect each other at right angles (90°). This splits the rhombus into four congruent right-angled triangles. Each side of the rhombus is the hypotenuse of one of these triangles, so we can use Pythagoras' theorem.

Solution:

1. Half of each diagonal: • 16 ÷ 2 = 8 cm • 12 ÷ 2 = 6 cm

2. Apply Pythagoras' theorem, with side s as the hypotenuse:

s² = 8² + 6² s² = 64 + 36 s² = 100 s = √100 = 10 cm

Answer: The side of the rhombus is 10 cm, which is option D.

Tip: When you see a rhombus with its diagonals given, always halve them first and think "right-angled triangle." Here 6, 8, 10 is a multiple of the 3-4-5 Pythagorean triple (×2). Spotting this triple saves time in the exam.