What is the inradius of a triangle with sides 7 cm, 8 cm, and 9 cm?

What is the inradius of a triangle with sides 7 cm, 8 cm, and 9 cm?

Step 1: Calculate the semi-perimeter (s) of the triangle. The semi-perimeter is found by adding all the sides together and dividing by 2. So, s = (7 cm + 8 cm + 9 cm) / 2.
Step 2: Calculate the semi-perimeter: s = (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.
Step 3: Calculate the area (A) of the triangle using Heron's formula. First, find the semi-perimeter (s) which we already calculated as 12 cm.
Step 4: Use Heron's formula: A = √(s * (s - a) * (s - b) * (s - c)), where a, b, and c are the sides of the triangle. Here, A = √(12 * (12 - 7) * (12 - 8) * (12 - 9)).
Step 5: Calculate A = √(12 * 5 * 4 * 3) = √(720) = 26 cm² (approximately).
Step 6: Now, use the formula for the inradius (r): r = A / s. We have A = 26 cm² and s = 12 cm.
Step 7: Calculate the inradius: r = 26 cm² / 12 cm = 2.1667 cm (approximately).

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