The diagonals of a rhombus are in the ratio 3 : 4 and its area is $384{\text{cm}}^2$. Find the length of each side in cm.

Let the diagonals be $3x$ and $4x$. Then ½ × $3x\times 4x=6x^2=384$, so $x^2=64$ and $x=8$, giving diagonals of 24 cm and 32 cm. The half-diagonals are 12 cm and 16 cm, so the side = √(144 + 256) = √400 = 20 cm.