Question

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

Answer 1

The length of the other side of the parallelogram is 11 cm.

Step-by-step explanation:

Let length of one side of a parallelogram = a = 17 cm

Let length of other side of a parallelogram = b

Length of one diagonal =  $D_{1}$ = 12 cm

Length of other diagonal = $D_{2}$ = 26 cm

In parallelogram, the sum of the squares of the diagonals = 2 x (the sum of the squares of the two adjacent sides)

=> $D_{1}^{2} + D_{2} ^{2} = 2(a^{2} + b^{2})$

=> $12^{2} + 26^{2} = 2(17^{2} + b^{2})$

=> 144 + 676 = 2(289 + $b^{2}$)

=> 820 = 578 + 2$b^{2}$

=> $2b^{2}$ = 820 - 578 = 242

=> $b^{2}$ = $\frac{242}{2}$ = 121

=> b = $\sqrt{121}$ = 11 cm

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