Question

ratio of diagonals of rhombus is 4:3 area is 96 find lengths of diagonals​

Answer 1

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Answer 2

We have been given that,

Ratio of the length of the diagonals is 4:3

Area of the rhombus is 96 cm²

We also know that the area of a rhombus is:-

$\dfrac{d_{1} \times d_{2}}{2}$

Here, d₁ and d₂ are the diagonals.

We can write the diagonals in the form:-

4x and 3x

So, according to question:-

96 = $\dfrac{4x \times 3x}{2}$

96 = $\dfrac{12x^{2}}{2}$

96 = 6x²

x² = 16

x = $\sqrt{16}$

x = 4 cm

So, the length of the diagonals is 16 cm and 12 cm respectively !