Question

An isosceles right triangle has area 8 cm^2 .Find the length of its hypotenious

Answer 1

$\textbf{Solution}$

Given, area of an isosceles right triangle = 8 cm2


Area of an isosceles triangle = 1/2 (Base x Height)

=>  8 = 1/2 (Base x Base)

[∴ base = height, because the given triangle is an isosceles triangle]

=> (Base)^2 =16

=>  Base= 4 cm

In ΔABC, using Pythagoras theorem

AC²= AB² + BC²= 42 + 42 = 16 + 16

=> AC ²= 32

=> AC = √32 cm

=> 4√2 cm

Thanks

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