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The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side is
  • a)
    22.4 cm
  • b)
    67.2 cm
  • c)
    44.8 cm
  • d)
    60 cm
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The sides of a triangle are in the ratio 13:14:15 and its perimeter is...
Ratio of sides = 13 : 14 : 15
Perimeter of triangle = 168 cm
Let the sides are 13x, 14x, and 15x
∴ 13x + 14x + 15x = 168
⇒ 42x = 168
⇒ x = 4
∴ sides are 13 x 4 = 52 cm
14 x 4 = 56 cm
15 x 4 = 60 cm
s = sum of sides/2 = 168/2 = 84

Let BL be altitude on the largest side AC of  ABC
Area of Δ ABC = 1344 cm2
⇒ 1/2 x base x altitude = 1344 cm2
⇒ 1/2 x AC x BL = 1344 cm2
⇒ 30 BL = 1344
⇒ BL = 1344/30 = 44.8 cm
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The sides of a triangle are in the ratio 13:14:15 and its perimeter is 168cm. The length of the altitude corresponding to the longest side isa)22.4 cmb)67.2 cmc)44.8 cmd)60 cmCorrect answer is option 'C'. Can you explain this answer?
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