Question

The sides of a triangle are 8cm, 10cm, and 14cm. Determine the radius of the inscribed circle.

Answer 1

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Answer 2

Given :

Sides of triangle :

8 , 10 and 14 cm

To find :

Radius of inscribed circle.

Solution :

The sides of triangle are

a = 8 cm

b = 10 cm

c = 14 cm

The semi perimeter of triangle s :

$\bf \: s = \frac{a + b + c}{2} \\ s = \frac{8 + 10 + 14}{2} = \frac{32}{2}$

So, Semi perimeter = 16 cm

According to Heron's formula,

The area of triangle :

$\bf \: A = \sqrt{s(s - a)(s - b)(s - c)}$

So, putting the values of sides a, b, c and Semi perimeter s

Area of triangle :

$\bf \: A = \sqrt{16(16 - 8)(16 - 10)(16 - 14)} \\ \bf \: A = \sqrt{16 \times 8 \times 6 \times 2} \\ \bf \: A = \sqrt{1536} = 39.19 \: {cm}^{2}$

Area of triangle with inscribed circle is:

$A \: = r \times s$

where

r = radius of inscribed circle.

s = semi perimeter

So

Putting the values of A and s in above equation

we get

$39.19 \: = r \times 16 \\ so \\ r = \frac{39.19}{16} = 2.45 cm$

So, the radius of inscribed circle r = 2.45 cm