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Question
The area of the rhombus is 576 sq.cm and the length of one of its diagonal is half of the length of the other diagonal then find the length of the diagonal
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Solution
Let one diagonal of the rhombus = d2 cm
The other diagonal d2 = `1/2` × d1 cm
Area of the rhombus = 576 sq.cm
`1/2` × (d1 × d2) = 576
`1/2` × (d1 × `1/2` d1) = 576
d1 × d1 = 576 × 2 × 2
= 6 × 6 × 4 × 4 × 2 × 2
d1 × d1 = 6 × 4 × 2 × 6 × 4 × 2
d1 = 6 × 4 × 2
d1 = 48 cm
d2 = `1/2` × 48 = 24 cm
∴ Length of the diagonals d1 = 48 cm and d2 = 24 cm.
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