# Is right triangle or not

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

Correct result:

A =  54.415

#### Solution:

$a=13 \ \\ b=11.5 \ \\ c=22.5 \ \\ \ \\ c_{1}=\sqrt{ a^2+b^2 }=\sqrt{ 13^2+11.5^2 } \doteq 17.3566 \ \\ c_{1}<>c \ \\ \ \\ s=\dfrac{ a+b+c }{ 2 }=\dfrac{ 13+11.5+22.5 }{ 2 }=\dfrac{ 47 }{ 2 }=23.5 \ \\ \ \\ A=\sqrt{ s \cdot \ (s-a) \cdot \ (s-b) \cdot \ (s-c) }=\sqrt{ 23.5 \cdot \ (23.5-13) \cdot \ (23.5-11.5) \cdot \ (23.5-22.5) }=3 \ \sqrt{ 329 }=54.415$

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