Euclid2

In the right triangle ABC with a right angle at C is given side a=29 and height v=17. Calculate the perimeter of the triangle.

Correct answer:

o =  85.78

Step-by-step explanation:

$$\begin{gathered} a=29 \\ h=17 \\ {a}^2=c_a^2+h^2 \\ {c}_a=\sqrt{a^2-h^2}=\sqrt{29^2-17^2}=2\sqrt{138}\doteq 23.4947 \\ {h}^2=c_a\cdot c_b \\ {c}_b={\displaystyle \frac{h^2}{c_a}}={\displaystyle \frac{17^2}{23.4947}}\doteq 12.3007 \\ c=c_a+c_b=23.4947+12.3007\doteq 35.7953 \\ {c}^2=a^2+b^2 \\ b=\sqrt{c^2-a^2}=\sqrt{35.7953^2-29^2}\doteq 20.9835 \\ o=a+b+c=29+20.9835+35.7953=85.78 \end{gathered}$$

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