Question

8.
The diagonals of a rhombus are in the ratio 3:5. If the area of the rhombus is 120 cm', find the
lengths of the diagonals of the rhombus,

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Answer 1

Given

• The diagonals of a rhombus are in the ratio 3:5. If the area of the rhombus is 120 cm.

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To find

• Length of the diagonals of the rhombus.

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Solution

• Let the ratio of diagonals be x.

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⇛ D1 = 3x

⇛ D2 = 5x

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• Area of rhombus is denoted as

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☆ Area = ½ × D1 × D2

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→ Area = 120

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→ ½ × 3x × 5x = 120

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→ 3x × 5x = 120 × 2

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→ 15x² = 240

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→ x² = 240/15

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→ x² = 16

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→ x = √16

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→ x = 4

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• By putting the value of x

⇛ D1 = 3x = 12

⇛ D2 = 5x = 20

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Hence,

• The length of diagonals of the rhombus are 12cm and 20cm.