Question

The perimeter of a rhombus is $100$ cm and one of its diagonals is $40$ cm . Then the area of the rhombus in square centimeters is

• A. $1200$
• B. $300$
• C. $600$
• D. $2500$

Answer 1

The correct option is C $600$

$Perimeterofarhombus=4a=100cm$
$\therefore a=25cm$
$Onediagonal{d}_1=40cm$
$a^2={\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2$
$or{25}^2={20}^2+{\left(\frac{d_2}{2}\right)}^2$

$or{\left(\frac{d_2}{2}\right)}^2=625-400$
$or\frac{d_2}{2}=15$
$or{d}_2=30cm$
$\therefore Areaofrhombus=\frac{1}{2}{d}_1{d}_2=\frac{1}{2}\times 40\times 30=600{cm}^2$