Question

If the diagonals of the rhombus are in the ratio 4:7 and the area is 504sqcm find the length of the diagonals​

Answer 1

Given :-

• The diagonals of the rhombus are in the ratio 4 : 7 and the area is 504 sq. cm.

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To Find :-

• The length of the diagonals.

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Let us assume :-

→ Smaller diagonal be 4x.

→ Bigger diagonal be 7x.

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Formula used :-

★ Area of a rhombus = (D₁ × D₂)/2

Where,

D₁ = Smaller diagonal of the rhombus

D₂ = Bigger diagonal of the rhombus

Finding the diagonals :

⟿ (4x × 7x)/2 = 504

⟿ 28x² = 504 × 2

⟿ 28x² = 1008

⟿ x² = 1008/28

⟿ x² = 36

⟿ x² = 6²

⟿ x = 6

∴ Diagonals are :

➽ Smaller diagonal = 4x = (4 × 6) = 24 cm

➽ Bigger diagonal = 7x = (7 × 6) = 42 cm