A triangle has sides with lengths of 3, 9, and 7. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-02-02T13:42:45

Radius of circle inscribed in a triangle $= \frac{A}{s}$ $=A/s$

Where,

$A$ $A$ =Area of triangle,

$s$ $s$ =Semi-perimeter of triangle $= \frac{a + b + c}{2}$ $=(a+b+c)/2$ Note $a, b, c$ $a,b,c$ are sides of the triangle

So, $s = \frac{3 + 9 + 7}{2} = \frac{19}{2} = 9.5$ $s=(3+9+7)/2=19/2=9.5$

We can find the area of triangle using Heron's formula:
Heron's formula:
$A r e a = \sqrt{s (s - a) (s - b) (s - c)}$ $Area = sqrt(s(s-a)(s-b)(s-c))$

$\to A r e a = \sqrt{9.5 (9.5 - 3) (9.5 - 9) (9.5 - 7)}$ $rarrArea=sqrt(9.5(9.5-3)(9.5-9)(9.5-7))$

$A r e a = \sqrt{9.5 (6.5) (0.5) (2.5)}$ $Area=sqrt(9.5(6.5)(0.5)(2.5))$

$A r e a = \sqrt{9.5 (8.12)}$ $Area=sqrt(9.5(8.12))$

$A r e a = \sqrt{77.14} = 8.78$ $Area=sqrt77.14=8.78$

$Radius=A/s=8.78/9.5=0.92...$