Question

One side of a rhombus is 20 cm long and one of its diagonals measures 24 cm. The area of the rhombus is

(a) 192 $c{m}^2$ (b) 480 $c{m}^2$ (c) 240 $c{m}^2$ (d) 384 $c{m}^2$

Answer 1

Diagonal $d_1=24cm$, Length of side $s=20cm$, Diagonal $d_2=x$.

By Pythagoras’ Theorem,

${20}^2=(\frac{d_1}{2}{)}^2+(\frac{x}{2}{)}^2$

$\Rightarrow 400=(\frac{24}{2}{)}^2+(\frac{x}{2}{)}^2$

$\Rightarrow 400=144+(\frac{x}{2}{)}^2$

$\Rightarrow x^2=\left(4\right)(400-144)=\left(4\right)\left(256\right)$

$\Rightarrow x=32cm$

Diagonal $d_2=32cm$.

Area of rhombus $=\frac{1}{2}\times 24\times 32=384c{m}^2$.