How do you find the lengths of the sides of a right triangle given the legs x and x and the hypotenuse 8?

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Answer 1 · 2016-03-07T12:16:08

#x=4sqrt2#

The Pythagorean Theorem gives the relations between the legs #a,b# and hypotenuse #c# of a right triangle:

#a^2+b^2=c^2#

Here, since the legs are both #x#, #a=x# and #b=x#, and since the hypotenuse is #8#, #c=8#.

#x^2+x^2=8^2#

Combine the #x^2# terms. Recall that #8^2=64#.

#2x^2=64#

Divide both sides by #2#.

#x^2=32#

Take the square root of both sides. (Only take the positive root--a negative side length wouldn't make any sense.)

#x=sqrt32#

Simplify the term in the square root.

#x=sqrt16sqrt2#

#x=4sqrt2#