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

User Mtsahakis
by
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1 Answer

4 votes

Answer:

  • 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
User MichalMoskala
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