RT leg and perimeter

Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.

Correct result:

a =  84
b =  73.4297
c =  111.5703

Solution:

$$\begin{gathered} a=84 \\ o=269 \end{gathered}$$

$$\begin{gathered} a^2+b^2=c^2 \\ a+b+c=o \\ 7056=c^2-b^2 \\ b+c=185 \\ 7056=c^2-(185-c{)}^2 \\ 7056=c^2-(185^2-2\cdot 185\cdot c+c^2) \\ 7056=-185^2+370c \\ 41281=370c \\ c=111.57 \\ b=185-c=73.4297 \end{gathered}$$

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