Question

Adjacent sides of a parallelogram are $11\text{cm}$ and $17\text{cm}$. If the length of one of its diagonals is $26\text{cm}$. Find the length of the other.

Answer 1

Sides of a parallelogram and diagonal of the parallelogram are related as:

${d_1}^2+{d_2}^2=2(a^2+b^2)$ where $a$ and $b$ are adjacent sides and $d_1$ and $d_2$ are diagonals.

Given $\Rightarrow$ $a=11\text{cm},b=17\text{cm}$ and $d_1=26\text{cm}$

Now by using the above given formula and given values,

$\begin{array}{cc}{26}^2+d_2^2& =2({11}^2+{17}^2)\\ 676+d_2^2& =2(121+289)\\ d_2^2& =144\\ d_2& =12\text{cm}\end{array}$

Hence, the length of the other diagonal of the parallelogram is equal to $12\text{cm}$.