Question

ABCD is a rhombus If area $\left(ABCD\right)=24c{m}^2$ and AC=8 cm, find the measure of the side of the rhombus.

• A. 5 cm
• B. 6 cm
• C. 7 cm
• D. 8 cm

Answer 1

The correct option is A

5 cm

Area of rhombus $=\frac{1}{2}\times$ (product of digonals)

$\frac{1}{2}\times AC\times BD=24$

$BD=\frac{24\times 2}{8}$

BD = 6 cm

In $\Delta OAB,OA=\frac{1}{2}AC=\frac{8}{2}=4cm$

$OB=\frac{1}{2}BD=\frac{6}{2}=3cm$

Also, $O{A}^2+O{B}^2=A{B}^2$

$\therefore A{B}^2=16+9=25$

$\therefore AB=\sqrt{25}=5$

So, sides of rhombus are 5 cm each.