Right triangle with legs 3 cm and 4 cm (hypotenuse 5 cm). Find the inradius (radius of the incircle).

Introduction / Context:The inradius r of a triangle satisfies r = A / s, where A is area and s is semiperimeter. For a right triangle with legs a and b and hypotenuse c, a standard shortcut is r = (a + b − c)/2.

Given / Assumptions:

• Legs a = 3, b = 4; hypotenuse c = 5.

Concept / Approach:Use r = (a + b − c)/2 or compute area and semiperimeter.

Step-by-Step Solution (method 1):r = (3 + 4 − 5)/2 = 2/2 = 1 cm.

Step-by-Step Solution (method 2):Area A = (1/2)*3*4 = 6.Semiperimeter s = (3 + 4 + 5)/2 = 6.r = A/s = 6/6 = 1 cm.

Verification / Alternative check:Both methods agree; the (3,4,5) right triangle is a well-known Pythagorean triple with inradius 1.

Why Other Options Are Wrong:Values 3.5, 1.75, 0.875 cm do not satisfy r = A/s for this triangle.

Common Pitfalls:Using r = c − (a + b)/2 (wrong ordering) or mixing formulas for circumradius and inradius.

Final Answer:1 cm