# Right isosceles

Calculate area of the isosceles right triangle which perimeter is 41 cm.

Correct result:

S =  72.1 cm2

#### Solution:

$o=41 \ \text{cm} \ \\ a=b \ \\ c=\sqrt{ a^2+b^2 }=\sqrt{ a^2+a^2 }=a \cdot \ \sqrt{ 2 } \ \\ o=a+b+c \ \\ o=2a+\sqrt{ 2 } \cdot \ a \ \\ a=\dfrac{ o }{ 2+\sqrt{ 2 } }=\dfrac{ 41 }{ 2+\sqrt{ 2 } } \doteq 12.0086 \ \text{cm} \ \\ \ \\ S=\dfrac{ a^2 }{ 2 }=\dfrac{ 12.0086^2 }{ 2 }=72.1 \ \text{cm}^2$

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