# Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm.

Result

S =  6096.4 cm2

#### Solution:

$p = 2a+b \ \\ \sin \gamma/2 = \dfrac{b/2}{ a } \ \\ b = 2a \sin \gamma/2 = 2a \sin 45^\circ \ \\ p = 2a + b = 2a + 2a \sin 45^\circ = 2a(1+\sin 45^\circ ) \ \\ \ \\ a = \dfrac{ p }{ 2 \cdot (1+\sin 45^\circ ) } = 110.421 \ \\ \ \\ S = \dfrac{1}{2} a^2 = \dfrac{1}{2} 110.421^2 = 6096.4 \ \text{cm}^2 \ \\$

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