Question

The perimeter of a rhombus is 40 cm and the length of one of its diagonals is 12 cm then the area of the rhombus is

• A. 95 $c{m}^2$
• B. 96 $c{m}^2$
• C. 97 $c{m}^2$
• D. 98 $c{m}^2$

Answer 1

The correct option is B 96 $c{m}^2$

Given the perimeter of rhombus is 40 cm and one diagonal is 12 cm

We know that perimeter of rhombus=$2\sqrt{p^2+q^2}$ where -p and q are diagonal of rhombus

$\therefore 40=2\sqrt{(12{)}^2+q^2}$

$\Rightarrow 20=\sqrt{144+q^2}$

$\Rightarrow 400=144+q^2$

$\Rightarrow q^2=400-144=256$

$\Rightarrow q=16$ cm

Then length of second diagonal is 16 cm

Then area of rhombus=$\frac{p\times q}{2}=\frac{12\times 16}{2}=\frac{192}{2}=96C{m}^2$