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A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes.

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The sides of a triangle are a = 35 cm, b = 54 cm and c = 61 cm

Now, perimeter a + b + c = 25 

⇒ S = 1/2 (35 + 54 + 61) 

⇒ s = 75 cm 

By using heron’s formula

The altitude will be a smallest when the side corresponding to it is longest Here, longest side is 61 cm.

Hence the length of the smallest altitude is 30.79 m

 

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