Question

Given the perimeter of rhombus is 40 cm and one diagonal is 12 cm .The length of second diagonal is

• A. 19 cm
• B. 18 cm
• C. 17 cm
• D. 16 cm

Answer 1

The correct option is D 16 cm

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