Question

Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is 14 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: 
$a^{2} + b^{2} =130cm^{2} \\ \\ d_{1} = 14 cm \:\:\:,d_{2} = ?$
    
2) We know that ,
In parallelogram ,

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

Hence,The length of other diagonal is 8 cm .

Answer 2

Answer:

8

Step-by-step explanation:

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

We know that a parallelogram is a quadrilateral whose opposite sides are parallel and equal and also angles are equal. Now we have the formula

  p ^2 + q ^2 = 2(a^2 + b^2) where p and q are diagonals and a, b are the parallel sides.

 14^2 + q^2 = 2(130)

  196 + q^2 = 260

       q^2 = 260 - 196

       q^2 = 64

        q = 8 cm