The length of a leg of an isosceles right triangle is #5sqrt2# units. What is the length of the hypotenuse?

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Answer 1 · 2018-03-27T14:29:57

hypotenuse = 10

You are given the leg length of one side, so you are basically given both leg lengths because an isosceles right triangle has two equal leg lengths:

#5sqrt2#

In order to find the hypotenuse you need to do
#a^2 +b^2 =c^2#

#a# = leg length 1
#b# = leg length 2
#c# = hypotenuse

#(5sqrt2)^2 + (5sqrt2)^2 = c^2#
#(25*2) +(25*2) = c^2#
#50+50 = c^2#
#100=c^2#
#sqrt100 = sqrt(c^2)#
#10 = c#
hypotenuse = 10