If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus.
Explanation:
We know that the diagonals of a rhombus bisect each other at right angles.
So, let’s assume that the two diagonals have lengths 6x and 8x.
⇒ (3x)2 + (4x)2 = 152
⇒ 25x2 = 225
⇒ x2 = 9
⇒ x = 3
∴ The length of the diagonals are 18 and 24.
∴ Area of the rhombus = ½ × product of the diagonals = ½ × 18 × 24 = 216
Hence, option (e).
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