Introduction to problem analysis triangle:

In this article we shall discuss about problem analysis triangle. Triangles contain three sides, which have two dimensions and it is closed. And triangles contain three vertices or three
corners. Here, triangle is depending on its interior, exterior angles and its sides. The types of triangle are obtuse triangle, acute triangle, right angle triangle, isosceles triangle,
scalene triangle and equilateral triangle.

Formula for Find the Area, Perimeter and Radius of Problem Analysis Triangle:

The Formula for find the area, perimeter and Radius of problem analysis triangle is given below that,

Formula for find the area of triangle:

Area of right triangle = `1/2 (b xx h)`

Where, b – Base

h – Height

Formula for find the perimeter of triangle:

Perimeter of a triangle = a + b + c

Where a, b and c are the length of the side.

Formula for find the Radius of triangle:

Radius of triangle (r) = `1/2 (sqrt(((b+c-a)(c+a-b)(a+b-c))/(a+b+c)))`

Where a, b and c are the length of the side.

Examples Based on Problem Analysis Triangle:

The example based on problem analysis triangle is given below that,

Example 1:

Establish the area of the triangle of base 6m and height 9m.

Solution:

Here, b = 6m; Height = 9m

So, area of the triangle = `1/2 (b xx h)`

= `1/2(6xx9)`

= 27m2

Example 2:

Establish the perimeter of the triangle of sides is 7cm, 8cm, and 9cm.

Solution:

Perimeter of the triangle = (Sum of the all sides)

= (7 + 8 + 6) cm

= 21cm

Example 3:

How do you find the radius of triangle? If triangle length of the sides are a = 8cm, b = 10cm and c = 12cm.

Solution:

Step 1:

The given triangle length of the sides are a = 8cm, b = 10cm and c = 12cm.

Step 2:

The Radius of triangle (r) = `1/2 (sqrt(((b+c-a)(c+a-b)(a+b-c))/(a+b+c)))`

Step 3:

Here, substitute the ‘a’, ‘b’ and ‘c’ values in radius of triangle formula.

Therefore, we get the value for Radius of triangle (r) = `1/2 (sqrt(((10+12-8)(12+8-10)(8+10-12))/(8+10+12)))`

Step 4:

We get the value for Radius of triangle (r) = `1/2 (sqrt(((14)(10)(6))/(30)))`

Radius of triangle (r) = `1/2 (sqrt((840)/(30)))`

Radius of triangle (r) = `1/2 (sqrt(28))`

Step 5:

Radius of triangle (r) = `1/2 (5.29)`

Radius of triangle (r) = 2.65cm.