Question

what is the radius of a circle in script in a triangle with side of length 12cm 35 cm and 37 cm​

Answer 1

Step-by-step explanation:

We have to find the radius of inscribed circle in a triangle with sides of length 12cm , 35 cm and 37 cm. solution : see diagram, let O is the centre of inscribed circle in a triangle ∆ABC. Therefore the radius of circle is 5cm.

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Answer 2

Given:

In triangle sides are given by,

12cm

35cm

37cm

To find:

Here, we need to find the radius of the incircle in triangle.

Solution:

a = 12 cm

b = 35 cm

c = 37 cm

Semi perimeter (S) = $\frac{a+b+c}{2}$

                          = $\frac{12 + 35 + 37}{2}$

                          = $\frac{84}{2}$

Semi perimeter (S) = 42 cm.

Area of triangle = $\sqrt{s (s-a)(s-b)(s-c)}$

Now, we will put the values and get the answer.

Area of triangle = $\sqrt{s (s-a)(s-b)(s-c)}$

                          = $\sqrt{42 (42 - 12) (42- 35)(42-37)}$

                          = $\sqrt{42 (30)(7)(5)}$

                          = $\sqrt{44100}$

                          = 210 cm²  

Area of triangle = 210 cm²  

Now, we need to find the radius of incircle.

Area of triangle =$\frac{1}{2}$ r ( a +b +c)  

210 cm² = $\frac{1}{2}$ r (12 + 35 + 37)

Now, we will simplify the terms

210 = $\frac{1}{2} r (84)$

210 = 42 r

r = $\frac{210}{42}$

r = 5 cm  

Therefore, the radius of the inscript is 5 cm.