Question

Find the radius of the in-circle of the triangle that sides, 25 cm, 51 cm, and 52 cm. Work is required

Answer 1

The radius of the incircle of the triangle with sides 25 cm, 51 cm, and 52

cm is 26 cm.

How can the radius of the incircle of a triangle be found?

The area of the triangle is given as follows;

A = √(s·(s - a)·(s - b)·(s - c))

Where;

a = 25 cm

b = 51 cm

c = 52 cm

s = The semi perimeter of the triangle = (25 + 51 + 52) ÷ 2 = 64

A = √(64·(64 - 25)·(64 - 51)·(64 - 52)) = 624

The area of the triangle is the area of ΔABC + ΔAOC + ΔBOC + ΔAOB

Which gives;

$A = \mathbf{\dfrac{a \cdot r}{2} + \dfrac{b \cdot r}{2} + \dfrac{c \cdot r}{2}}$

Therefore;

$A = r \cdot \left(\dfrac{a + b + c }{2} \right) = \mathbf{r \cdot s}$

$r = \dfrac{A}{s}$

Therefore;

$r = \dfrac{624}{64} = 26$

The radius of the incircle of the triangle is 26 cm

Learn more about the incircle of a triangle here:

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