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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.
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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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