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Question
One of the diagonals of a rhombus is thrice as the other. If the sum of the length of the diagonals is 24 cm, then find the area of the rhombus.
Solution
Let one of the diagonals of rhombus be ‘d1’ cm and the other be d2 cm.
Give d1 = 3 × d2
Also d1 + d2 = 24 cm
⇒ 3d2 + d2 = 24
4d2 = 24
d2 = `24/4`
d2 = 6 cm
d1 = 3 × d2 = 3 × 6
d1 = 18 cm
∴ Area of the rhombus = `1/2` × d1 × d2 sq.units
= `1/2` × 18 × 6 cm2
= 54 cm2
Area of the rhombus = 54 cm2
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