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A triangle with sides of 25 cm, 52 cm, and 63 cm has a second triangle drawn inside it with all its sides at a distance of 3 cm from the sides of the original triangle. Find the area of the inner triangle.

 Oct 29, 2021
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Triangle => ABC            inner triangle => A'B'C'

 

s = 1/2(25+52+63) = 70

 

A = 630 cm2

 

r = A / s = 9

 

Similarity coefficient = (r - 3) /  r        =>   6/9  = 2/3

 

[A'B'C'] = A * (2/3)2 = 630 * (4/9) = 280

 Oct 31, 2021

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