Question

The length of one side of a parallelogram is $17cm.$ If the length of its diagonals is $12cm$ and $26cm$, then find the length of the other side of a parallelogram.

Answer 1

In parallelogram $ABCD,$

$\begin{array}{cc}{d}_1^2+d_2^2& =2\left(a^2+b^2\right)\\ {26}^2+{12}^2& =2\left({17}^2+b^2\right)\\ 676+144& =2\left(289+b^2\right)\\ b^2+289& =\frac{820}{2}\\ b^2& =410-289\\ b^2& =121\\ b& =\sqrt{121}\\ & =11cm\end{array}$

Hence, the length of the other side of the parallelogram is equal to $11cm.$