Question

sum of square of adjacent sides of a parallelogram is 130 sq cm and length of one of its diagonal is 14cm. Find the length of other diagonal

Answer 1

Given :

• In a parallelogram,

1. Sum of square of adjacent sides = 130 sq cm
2. Length of one diagonal = 14 cm

To find :

• Length of the other diagonal

Solution :

• Let the length of the two adjacent sides of the parallelogram be x and y.
• Let the length of the two diagonals be a and b.
• We know that, in a parallelogram, the sum of squares of the diagonals is equal to twice the sum of squares of the adjacent sides.

     ∴ a² + b² = 2( x² + y² )

• Substituting the given values,

        14² + b² = 2( 130 )

     ∴ b² = 260 - 196

     ∴ b² = 64

     ∴ b = 8 cm

Answer : The length of the other diagonal will be 8 cm.