Question

The length of the diagonals of a rhombus is in the ratio 4:3.if its area is 384 cm.find its side

Answer 1

Let the diagonals be 4x and 3x. Therefore,  Area=1/2*4x*3x =>384=6x^2 =>x^2=64 =>x=8  Therefore the diagonals are 32cm and 24cm long.  

Answer 2

Answer:

Here ,

Let Diagonal 1 (d₁ ) = 4x

And Diagonal 2 (d₂ ) = 3x

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As we know that

Area of a rhombus = $\frac{1}{2}$ × d₁ ₓ d₂

→ 384 = $\frac{1}{2}$ × 4x × 3x

→ 384 × 2 = 12x²

→ 768 = 12x²

→ x² = $\frac{768}{12}$

→ x² = 64

→ x = √64

→ x = 8

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Then ,

d₁ = 4x = 4 × 8 = 32 cm

d₂ = 3x = 3 × 8 = 24 cm

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In each triangle formed in the rhombus the length of diagonals will become half

Let the side be y

By pythagoras theorm :

16² + 12² = y²

256 + 144 = y²

y² = 400

y = √400

y = 20 cm