Right isosceles

Calculate area of the isosceles right triangle which perimeter is 26 cm.

Correct result:

S =  29 cm²

Solution:

$$\begin{gathered} o=26\text{ cm } \\ a=b \\ c=\sqrt{a^2+b^2}=\sqrt{a^2+a^2}=a\cdot \sqrt{2} \\ o=a+b+c \\ o=2a+\sqrt{2}\cdot a \\ a={\displaystyle \frac{o}{2+\sqrt{2}}}={\displaystyle \frac{26}{2+\sqrt{2}}}\doteq 7.6152\text{ cm } \\ S={\displaystyle \frac{a^2}{2}}={\displaystyle \frac{7.6152^2}{2}}=29{\text{cm}}^2 \end{gathered}$$

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