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What is the radius of the circle inscribed in triangle ABC$ if AB = 15, AC = 41, and BC = \(42\)?

 Apr 14, 2022

Best Answer 

 #1
avatar+578 
+2

The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:

 

We can find the semi perimeter by adding all the known sides and dividing by 2.

 

That would be (15+41+42)/2 = 98/2 = 49

 

We can find the area of the triangle using the heron's formula:

 

sqrt(49(49-15)(49-41)(49-42))

 

= 28*sqrt(119) = approx 305.44393

 

Substituting that in the Area of triangle/semi perimeter of the triangle formula:

 

28*sqrt(119)/49

 

= (4sqrt(17))/sqrt(7) or approx.  6.23354 units

 

If you want, rationalise the radical. Its up to you wink

 

-Vinculum

 

smileysmileysmiley

 Apr 14, 2022
edited by Vinculum  Apr 14, 2022
 #1
avatar+578 
+2
Best Answer

The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:

 

We can find the semi perimeter by adding all the known sides and dividing by 2.

 

That would be (15+41+42)/2 = 98/2 = 49

 

We can find the area of the triangle using the heron's formula:

 

sqrt(49(49-15)(49-41)(49-42))

 

= 28*sqrt(119) = approx 305.44393

 

Substituting that in the Area of triangle/semi perimeter of the triangle formula:

 

28*sqrt(119)/49

 

= (4sqrt(17))/sqrt(7) or approx.  6.23354 units

 

If you want, rationalise the radical. Its up to you wink

 

-Vinculum

 

smileysmileysmiley

Vinculum Apr 14, 2022
edited by Vinculum  Apr 14, 2022
 #2
avatar+69 
+1

When it is rationalised, it is (4sqrt(119))/7

ch1ck3n  Apr 14, 2022

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