# 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.

Result

S =  450 cm2

#### Solution:

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

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