Perpendicular 70824

One perpendicular to the ABC right triangle has a length a = 14 cm, and a radius of the circle inscribed in this triangle r = 5 cm. Find the size of the diaphragm and its second perpendicular.

Correct answer:

c =  26.5 cm
b =  22.5 cm

Step-by-step explanation:

$$\begin{gathered} a=14\text{cm} \\ r=5\text{cm} \\ b=\frac{2\cdot r\cdot (a-r)}{a-2\cdot r}=\frac{2\cdot 5\cdot (14-5)}{14-2\cdot 5}=\frac{45}{2}=22.5\text{cm} \\ c=\sqrt{a^2+b^2}=\sqrt{14^2+22.5^2}=\frac{53}{2}\text{cm}=26.5\text{cm} \end{gathered}$$

$$\begin{gathered} \text{ Verifying Solution: } \\ s=(a+b+c)/2=(14+\frac{45}{2}+\frac{53}{2})/2=\frac{63}{2}=31.5\text{cm} \\ S=a\cdot b/2=14\cdot \frac{45}{2}/2=\frac{315}{2}=157.5{\text{cm}}^2 \\ {r}_2=S/s=\frac{315}{2}/\frac{63}{2}=\frac{315}{2}:\frac{63}{2}=\frac{315}{2}\cdot \frac{2}{63}=\frac{315\cdot 2}{2\cdot 63}=\frac{630}{126}=5\text{cm} \\ b=\frac{45}{2}\text{cm}=\frac{45}{2}\text{cm}=22.5\text{cm} \end{gathered}$$

Try calculation via our triangle calculator.

Try another example