The length of a leg of an isosceles right triangle is #5sqrt2#. How do you find the length of the hypotenuse?

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Answer 1 · 2016-01-06T16:12:27

The hypotenuse
#AB = 10 cm#

The above triangle is a right angled isosceles triangle , with #BC = AC#

The length of the leg given #=5sqrt2cm# (assuming units to be in cm)

So, #BC = AC = 5sqrt2 cm#

The value of the hypotenuse #AB# can be calculated using the Pythagoras theorem:

#(AB)^2 = (BC)^2 +(AC)^2#

#(AB)^2 = (5sqrt2)^2 +(5sqrt2)^2#

#(AB)^2 = 50 +50#

#(AB)^2 = 100#

#(AB) = sqrt100#

#AB = 10 cm#