A triangle has sides with lengths of 3, 9, and 8. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-03-05T23:45:12

Heron's formula states that
Area = $\sqrt{s (s - a) (s - b) (s - c)}$ $sqrt(s(s-a)(s-b)(s-c))$

Where s is the sum of all sides / 2 (Also known as the semiperimeter)
a,b,c are the side lengths

From here, you can just plug in all the values.
Find that s = 10
Area = $\sqrt{10 (7) (1) (2)}$ $sqrt(10(7)(1)(2))$
Get $\sqrt{140}$ $sqrt140$

Now, we use the formula that says that

Area = semiperimeter * inradius

So we have

$\sqrt{140} = 10 \cdot$ $sqrt140 = 10 *$ radius

Therefore, the radius is $\frac{\sqrt{140}}{10}$ $sqrt140 / 10$

We can simplify the radical and cancel out to get

$\frac{\sqrt{35}}{5}$ $sqrt35 / 5$