Respuesta :

Answer:

150 cm²

Step-by-step explanation:

Given

  • Perimeter = 60 cm
  • Hypotenuse = 25 cm

Solving

  • We need to find the lengths of the altitudes
  • Since 25 cm is already covered there is (60 - 25) = 35 cm remaining
  • The lengths can be taken as x and 35 - x
  • Now, since it's a right triangle, we can solve for x using the Pythagorean Theorem

Applying the theorem

  • x² + (35 - x)² = 25²
  • x² + 1225 - 70x + x² = 625
  • 2x² - 70x + 600 = 0
  • x² - 35x + 300 = 0
  • x = 35 ± √1225 - 4(1)(300) / 2
  • x = 35 ± √25 / 2
  • x = 35 ± 5 / 2
  • x = 40/2 = 20 or x = 30/2 = 15
  • Upon solving the lengths of the altitudes are 15 and 20

Area of the triangle

  • 1/2 x product of the altitudes
  • 1/2 x 15 x 20
  • 10 x 15
  • 150 cm²

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