Is right triangle or not

If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.

Correct result:

A =  54.4151

Solution:

$$\begin{gathered} a=13 \\ b=11.5 \\ c=22.5 \\ {c}_1=\sqrt{a^2+b^2}=\sqrt{13^2+11.5^2}\doteq 17.3566 \\ {c}_1<>c \\ s={\displaystyle \frac{a+b+c}{2}}={\displaystyle \frac{13+11.5+22.5}{2}}={\displaystyle \frac{47}{2}}=23\frac{1}{2}=23.5 \\ A=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}=\sqrt{23.5\cdot (23.5-13)\cdot (23.5-11.5)\cdot (23.5-22.5)}=3\sqrt{329}=54.4151 \end{gathered}$$

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