Question

The diagonals of the parallelogram are equal to 17 and 19, and the sides are proportional to each other as 2:3, Find sides.

Answer 1

• 10 and 15 units

Explanation:

Given:

• d₁ = 17
• d₂ = 19
• a = 2x
• b = 3x

Use the relationship between diagonals and sides of the parallelogram:

• d₁² + d₂² = 2(a² + b²)

Substitute and solve for x:

• 17² + 19² = 2((2x)² + (3x)²)
• 650 = 2(4x² + 9x²)
• 325 = 13x²
• x² = 325/13
• x² = 25
• x = 5

Find the sides:

• a = 2x = 2*5 = 10
• b = 3x = 3*5 = 15