Question

The adjacent sides of a parallelogram are $15cm$ and $10cm$. If length of one diagonal of this parallelogram is $20cm$, the length of other diagonal will be:

• A. $30cm$
• B. $5\sqrt{10}cm$
• C. $10\sqrt{5}cm$
• D. $4\sqrt{30}cm$

Answer 1

Answer: (B)

$5\sqrt{10}cm$

The sum of the square of the diagonals of a parallelogram is the sum of the square of its sides. So,

${20}^2+d^2={15}^2+{10}^2+{15}^2+{10}^2$

now,

$d^2={15}^2+{10}^2+{15}^2+{10}^2-{20}^2$

$d=\sqrt{{15}^2+{10}^2+{15}^2+{10}^2-{20}^2}$

$d=\sqrt{2\times {15}^2+2\times {10}^2-{20}^2}$

$d=\sqrt{450+200-400}$

$d=\sqrt{450-200}$

$d=\sqrt{250}$

$d=5\sqrt{10}cm$