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in Perimeter and Area of Plane Figures by (23.5k points)
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What is the radius of a circle inscribed in a triangle having side lengths 35 cm, 44 cm and 75 cm? 

(a) 3 cm 

(b) 4 cm 

(c) 5 cm 

(d) 6 cm

1 Answer

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Best answer

(d) 6 cm

Let a = 35 cm, b = 44 cm, c = 75 cm. Then

s = \(\frac{a+b+c}{2}\) = \(\frac{34+44+75}{2}\) cm = 77 cm

∴ Area if triangle = \(\sqrt{77(77-35)(77-44)(77-75)}\) cm2

\(\sqrt{77\times42\times33\times2}\) cm2

= (7 x 11 x 6 ) cm= 462 cm2

∴ Radius of incircle = \(\frac{\text{Area}}{\text{semi-perimeter}}\) = \(\frac{462}{77}\) cm = 6 cm.

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