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..

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step-by-step explanation:

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1