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MHT CET202519 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

The ratios of sides in a triangle A B C are 5: 12: 13 and its area is 270 . Then sides of the triangle are

Options

  1. A5,12,13
  2. B10,24,26
  3. C15,36,39
  4. D20,48,52

Correct answer

C. 15,36,39

Step-by-step solution

The sides of the triangle are in the ratio 5:12:13 . Since 5^2 + 12^2 = 169 , which equals 13^2 , the triangle is right-angled with perpendicular sides proportional to 5 and 12. Taking the sides as 5x , 12x , and 13x , the area is computed using the formula for a right triangle: 1 2 base height = 1 2 5x 12x = 30x^2 . Given the area equals 270, set 30x^2 = 270 ⇒ x^2 = 9 ⇒ x = 3 (since side lengths are positive). Substituting back, the sides are 5 3 = 15 , 12 3 = 36 , and 13 3 = 39 . These values correspond to option

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