Question

The length of the diagonals of a rhombus is in the ratio 4 : 3. If its area is $384c{m}^2$, find its side.

Answer 1

Let the lengths of the diagonals of rhombus are 4x, 3x.

$\therefore$ Area of the rhombus $=\frac{1}{2}$

(Product of its diagonals)

$=\frac{1}{2}(4x\times 3x)=384$ (given)

$\Rightarrow 6x^2=384\Rightarrow x^2=64$

$\Rightarrow x=8cm$

$\therefore$ Diagonals are $4\times 8=32$ cm and 3(8)=24 cm.

$\therefore$ OC =16 cm and OD =12 cm

$\therefore$ Side $DC=\sqrt{O{C}^2+O{D}^2}$

$\therefore$ Side $DC=\sqrt{{16}^2+{12}^2}$

[By Pythagoras Theorem in $\Delta DOC]$

$=\sqrt{256+144}=\sqrt{400}=20cm$

Hence, side of the rhombus =20 cm.