Question

The area of a rhombus one side of which measures 20 cm and one of whose diagonals is 24 cm, is -

• A. $344c{m}^2$
• B. $324c{m}^2$
• C. $364c{m}^2$
• D. $384c{m}^2$

Answer 1

The correct option is D $384c{m}^2$

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