Consider a isosceles right triangle with hypotenuse length of 10. Exactly how long are the legs?

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Answer 1 · 2016-01-11T16:27:54

So the length of the legs $BC =AC = 5sqrt2 cm$

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The length $AB = 10 cm$ (hypotenuse)

(note: assuming units to be in cm)

Applying the Pythagoras theorem
$AB^2 = BC ^2 + AC^2$

$10^2 = BC ^2 + AC^2$

but $BC =AC$ (Because the triangle is isosceles)

$100 = 2 AC ^2$

$AC ^2 = 100/2$

$AC ^2 = 50$

$AC =sqrt 50$

$AC =5sqrt 2$

So the length of the legs $BC =AC = 5sqrt2 cm$