RT - inscribed circle

In a rectangular triangle with sides lengths> a = 30cm and b = 12.5cm, the right angle is at vertex C. Calculate the radius of the inscribed circle.

Correct answer:

r =  5 cm

Step-by-step explanation:

$$\begin{gathered} a=30\text{cm} \\ b=12.5\text{cm} \\ c=\sqrt{a^2+b^2}=\sqrt{30^2+12.5^2}=\frac{65}{2}=32.5\text{cm} \\ S=\frac{a\cdot b}{2}=\frac{30\cdot 12.5}{2}=\frac{375}{2}=187.5{\text{cm}}^2 \\ s=(a+b+c)/2=(30+12.5+32.5)/2=\frac{75}{2}=37.5\text{cm} \\ r=S/s=\frac{375}{2}/\frac{75}{2}=\frac{375}{2}:\frac{75}{2}=\frac{375}{2}\cdot \frac{2}{75}=\frac{375\cdot 2}{2\cdot 75}=\frac{750}{150}=5\text{cm} \end{gathered}$$

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