The diagonals of a rhombus are in the ratio $3:4$ and its area is $96 \text{ cm}^{2}$. The lengths of the…
The diagonals of a rhombus are in the ratio $3:4$ and its area is $96 \text{ cm}^{2}$. The lengths of the diagonals are:
$8$ cm and $12$ cm
$12$ cm and $16$ cm
$6$ cm and $8$ cm
$9$ cm and $12$ cm
Solution
Let diagonals be $3k$ and $4k$. Area $= \dfrac{1}{2}(3k)(4k) = 6k^{2} = 96 \Rightarrow k^{2} = 16 \Rightarrow k = 4$. Diagonals are $12$ cm and $16$ cm.