RT = legs, circle

One leg of a right triangle ABC has length a= 14 cm and the radius of the circle inscribed in this triangle r= 5 cm. Calculate the length of the hypotenuse and its other leg.

Correct answer:

c =  26.5 cm
b =  22.5 cm

Step-by-step explanation:

$$\begin{gathered} a=14\text{cm} \\ r=5\text{cm} \\ b=\frac{2\cdot r\cdot (a-r)}{a-2\cdot r}=\frac{2\cdot 5\cdot (14-5)}{14-2\cdot 5}=\frac{45}{2}=22.5\text{cm} \\ c=\sqrt{a^2+b^2}=\sqrt{14^2+22.5^2}=26.5\text{cm} \end{gathered}$$

$$\begin{gathered} \text{ Verifying Solution: } \\ s=(a+b+c)/2=(14+22.5+26.5)/2=\frac{63}{2}=31.5\text{cm} \\ S=\frac{a\cdot b}{2}=\frac{14\cdot 22.5}{2}=\frac{315}{2}=157.5{\text{cm}}^2 \\ {r}_2=S/s=157.5/31.5=5\text{cm} \\ b=22.5\text{cm}=22.5\text{cm} \end{gathered}$$

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