Question

If the sum of the diagonal of a rhombus is $10cm$ and its perimeter is $4\sqrt{13}cm$, then the lengths of its diagonals are

• A. $5cm$, $5cm$
• B. $6cm$, $4cm$
• C. $7cm$, $3cm$
• D. $8cm$, $2cm$

Answer 1

Answer: (B)

$6cm$, $4cm$

Given that:

Perimeter of a rhombus$=4\sqrt{12}cm$

Sum of diagonals$=10cm$

Let $d_1$ and $d_2$ be diagonals of the rhombus.

$d_1+d_2=10$..............................(i)

Length of the side of rhombus$=\frac{4\sqrt{12}}{4}cm=\sqrt{12}cm$

Area of the rhombus$=(\sqrt{12}{)}^2=12c{m}^2$

Area of the rhombus $=\frac{1}{2}\times d_1\times d_2=12c{m}^2$

or, $d_1{d}_2=24$ ..........(ii)

On solving eqn.(i) and (ii), we get

$d_1=6cm$ and $d_2=4cm$

Hence, B is the correct option.