Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm². Calculate content of square over the triangle's hypotenuse.

Correct answer:

S =  450 cm²

Step-by-step explanation:

$$\begin{gathered} 900=a^2+b^2+c^2 \\ {c}^2=a^2+b^2 \\ 900=c^2+c^2 \\ 2c^2=900 \\ c=\sqrt{900\mathrm{/}2}=15\sqrt{2}\text{ cm}\doteq 21.2132\text{ cm } \\ S=900\mathrm{/}2=450{\text{cm}}^2 \end{gathered}$$

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