Question
The length of the diagonal of a rhombus is 24 cm, and
the perimeter is 80 cm. Find the area of the rhombus.Solution
Let the side of the rhombus be a. Given: Perimeter = 80 cm, so 4a = 80 a = 20 cm. Let the diagonals of the rhombus be dâ = 24 cm and dâ. We know that the diagonals of a rhombus bisect each other at right angles, so we can use Pythagoras' theorem: a² = (dâ/2)² + (dâ/2)² 20² = (24/2)² + (dâ/2)² 400 = 12² + (dâ/2)² 400 = 144 + (dâ/2)² (dâ/2)² = 256 dâ/2 = 16, so dâ = 32 cm. Area of the rhombus = 1/2 Ă dâ Ă dâ Area = 1/2 Ă 24 Ă 32 = 384 cm². Correct option: C) 384 cm²
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