The diagonals of a rhombus are 16cm and 30cm long. What is the perimeter of the rhombus

Analyze the question: We are given the two diagonals of a rhombus (16 cm and 30 cm) and asked for its perimeter.

Concept: The diagonals of a rhombus bisect each other at right angles (90°). This splits the rhombus into 4 congruent right-angled triangles. Each side of the rhombus is the hypotenuse of one of these triangles.

Solution:

1. Half of each diagonal: • 16 ÷ 2 = 8 cm • 30 ÷ 2 = 15 cm

2. Use Pythagoras' theorem to find one side (s): s² = 8² + 15² s² = 64 + 225 = 289 s = √289 = 17 cm

3. A rhombus has 4 equal sides, so: Perimeter = 4 × 17 = 68 cm

Tip: Memorize the Pythagorean triple 8-15-17 (along with 3-4-5, 5-12-13, 7-24-25). Spotting it saves time in the exam. For any rhombus question with diagonals d₁ and d₂, the side is √((d₁/2)² + (d₂/2)²), and the perimeter is 4 times that.