Question

The perimeter of a rhombus is 100 cm. If one of its diagonal is 14 cm, then the area of the rhombus is:

• A. 144 sq. cm
• B. 225 sq.cm
• C. 336 sq. cm
• D. 400 sq. cm

Answer 1

The correct option is C 336 sq. cm

Perimeter of rhombus=100 cm

$\therefore$one side of rhombus$=\frac{100}{4}=25cm$

Since diagonal of a rhombus bisect each other at right angle

$\therefore AO=\frac{1}{2}\times 14=7cm.and\angle AOB={90}^{\circ }$

In $\Delta AOB$

$OB=\sqrt{A{B}^2-A{O}^2}$

$OB=\sqrt{{25}^2-7^2}$

$OB=\sqrt{625-49}$

$OB=\sqrt{576}$

$OB=24cm$

$\therefore$ Length of other diagonal$=2\times OB=2\times 24=48cm$

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

$\Rightarrow \frac{1}{2}\times 48\times 14=336sq.cm$