Cathethus and the inscribed circle

A right triangle is given one cathetus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.

Correct answer:

S =  157.5 cm²

Step-by-step explanation:

$$\begin{gathered} a=14\text{cm} \\ r=5\text{cm} \\ b=\frac{2\cdot r\cdot (a-r)}{a-2\cdot r}=\frac{2\cdot 5\cdot (14-5)}{14-2\cdot 5}=\frac{45}{2}=22.5\text{cm} \\ S=\frac{a\cdot b}{2}=\frac{14\cdot 22.5}{2}=157.5{\text{cm}}^2 \end{gathered}$$

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