The diagonal of a rhombus are 12cm and 5cm. calculate its perimeter

Analyze the question We have a rhombus with diagonals 12 cm and 5 cm, and we need its perimeter.

Concept The diagonals of a rhombus bisect each other at right angles. This splits the rhombus into 4 congruent right-angled triangles. Each triangle has legs equal to half of each diagonal, and its hypotenuse is a side of the rhombus.

Solution

• Half of the first diagonal = 12 ÷ 2 = 6 cm
• Half of the second diagonal = 5 ÷ 2 = 2.5 cm

Side of the rhombus (Pythagoras): s² = 6² + 2.5² s² = 36 + 6.25 = 42.25 s = √42.25 = 6.5 cm

Perimeter = 4 × s = 4 × 6.5 = 26 cm

Answer The perimeter is 26 cm, which is option A.

Tip Look out for the 5-12-13 Pythagorean triple. Here the full diagonals are 5 and 12, so the side is half of 13, which is 6.5 cm. The perimeter is then 4 × 6.5 = 26 cm. Recognising common triples (3-4-5, 5-12-13, 8-15-17) saves a lot of time in exams.