Question

Find the area of rhombus whose perimeter is $100m$ and one of whose diagonal is $30m$.

• A. $600m^2$
• B. $500m^2$
• C. $3000m^2$
• D. none of these

Answer 1

The correct option is A $600m^2$

Perimeter of Rhombus is $100m$

Side of Rhombus is $\frac{100}{4}=25$

By pytagorous theorm

The other diagonal is

${\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2=a^2$

${15}^2+{\left(\frac{d_2}{2}\right)}^2={25}^2$

$225+{\left(\frac{d_2}{2}\right)}^2=625$

${\left(\frac{d_2}{2}\right)}^2=400$

$\left(\frac{d_2}{2}\right)=20$

$d_2=40$

The area of Rhombus is $\frac{1}{2}\times d_1\times d_2$

$⟹\frac{1}{2}\times 40\times 30$

$⟹600m^2$