Question

The diagonals of the parallelogram are 10 and 12. One of its sides is 9 cm. Find the second side.

Answer 1

• 6.4 cm

Explanation:

Given:

• d₁ = 10 cm
• d₂ = 12 cm
• a = 9 cm
• b = ?

We know that the sum of squares of diagonals of the parallelogram is equal to twice the sum of the squares of the sides:

• d₁² + d₂² = 2(a² + b²)

Substitute the values and solve for b:

• 10² + 12² = 2(9² + b²)
• 100 + 144 = 2(81 + b²)
• 122 = 81 + b²
• b² = 41
• b = √41
• b = 6.4 cm