Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 252 cm.

Correct answer:

S =  2723.9 cm²

Step-by-step explanation:

$$\begin{gathered} p=2a+b \\ \sin \gamma \mathrm{/}2={\displaystyle \frac{b\mathrm{/}2}{a}} \\ b=2a\sin \gamma \mathrm{/}2=2a\sin 45\mathrm{°} \\ p=2a+b=2a+2a\sin 45\mathrm{°}=2a(1+\sin 45\mathrm{°}) \\ a={\displaystyle \frac{p}{2\cdot (1+\sin 45\mathrm{°})}}=73.809 \\ S={\displaystyle \frac{1}{2}}{a}^2={\displaystyle \frac{1}{2}}73.809^2=2723.9{\text{cm}}^2 \end{gathered}$$

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