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#

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#