Question

Sum of the squares of adjacent sides of a parallelogram is 130 cm and length of one of its diagonals is 14 cm. Find the length of the other diagonal.

Answer 1

Let ABCD be the given parallelogram and its diagonals AC and BD intersect at point M.

∴ AB² + AD² = 130cm, BD = 14cm

MD = 1/1 BD (i) [Diagonals of a parallelogram bisect each other] 

= 1/2 × 14 = 7 cm 

In ∆ABD, seg AM is the median. [From (i)] 

∴ AB² + = 2AM² + 2MD² [Apollonius theorem] 

∴ 130 = 2 AM² + 2(7)² 

∴ 65 = AM² +49 [Dividing both sides by 2] 

∴ AM² = 65 – 49 

∴ AM² = 16 [Taking square root of both sides] 

∴ AM = √16

= 4cm

Now, AC =2 AM [Diagonals of a parallelogram bisect each other] 

2 × 4 = 8 cm 

∴ The length of the other diagonal of the parallelogram is 8 cm.