Question

Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is14 cm. Find the length of the other diagonal.

Answer 1

Final Answer:  8cm 

Steps:

1)  Let a,b be two adjacent sides of a parallelogram & $d_{1}$ and $d_{2}$ be two diagonals of a parallelogram .
 
Given: 
[tex]a^{2} + b^{2} =130cm^{2} \\ \\ d_{1} = 14 cm \:\:\:,d_{2} = ? [/tex]
    
2) We know that ,
In parallelogram ,

[tex]d_{1}^{2}+d_{2}^{2}=2(a^{2} + b^{2}) \\ \\ =\ \textgreater \ 14^{2} + d_{2}^{2}= 2*130 \\ \\ =\ \textgreater \ d_{2}^{2}= 260 - 196=64 \\ \\ =\ \textgreater \ d_{2} = 8 cm [/tex]

Hence,The length of other diagonal is 8 cm .

Answer 2

SOLUTION :
Let the sides of a parallelogram are PS, SR, QR, PQ & diagonals be PR & QS.

Given : Sum of the squares of adjacent sides of a parallelogram (PS² + SR²)& (QR² + PQ²) = 130 cm & length of one of its diagonals (PS) = 14 cm.

(PS² + SR²)+ (QR² + PQ²) = PR² + QS²
[the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.]

130 +130 = 14² + QS²
260 = 196 + QS²
260 - 196 = QS²
64 = QS²
QS =√64 = 8 cm
QS = 8 cm

Hence, the length of the other diagonal is 8 cm.

HOPE THIS WILL HELP YOU…..