What is the radius of the circle inscribed in triangle $abc$ if $ab = 5, ac=6, bc=7$? express your answer in simplest radical form?

You can use the area method. First of all, find s that is half of perimeter:

un.

Then:

1. Find the area of triangle using Heron's fofmula:

sq. un.

2. Find the area of triangle using the formula , where r is the radius of inscribed circle.

sq. un.

3. Equate both expressions:

un.

un.

General Idea:

There are two formula's to find the area of triangle when three sides are given.

FIRST FORMULA: When a, b and c are the three sides of the triangle, we can use the Heron's triangle to find the Area of triangle.

SECOND FORMULA: When the circle is inscribed in a triangle with radius r, then we can use the below formula to find the Area of triangle.

Applying the concept:

In our problem we are given the side lengths of triangle as 5, 6, & 7

Area of triangle using first formula:

Area of triangle using second formula:

Conclusion:

We need to set up an equation based on the results that we get when finding the area of triangle using first and second formula, we get..

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point