Question

The area of rhombus is 216 sq. cm. If its one diagonal is 24 cm, find length of its side.

• A. 15 cm
• B. 10 cm
• C. 18 cm
• D. 9 cm

Answer 1

Answer: (A)

15 cm

The one diagonal $d_1=24cm$

Area of rhombus=$216sq.cm$

Since,

Area of rhombus$=\frac{1}{2}\times d_1\times d_2$

$\Rightarrow 216=\frac{1}{2}\times 24\times d_2$

$\Rightarrow 216=12\times d_2$

$\Rightarrow \frac{216}{12}=d_2$

$\Rightarrow d_2=18cm$

Side of rhombus=$\sqrt{{\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2}$

$=\sqrt{{\left(\frac{24}{2}\right)}^2+{\left(\frac{18}{2}\right)}^2}$

$=\sqrt{{12}^2+9^2}$

$=\sqrt{144+81}$

$=15cm$

$SideofRhombus=15cm$