Question

The hypotenuse of an isosceles right triangle is 8 inches. Find the length of the legs.

Answer 1

Are the legs of equal length?

Answer 2

Since the triangle is an isosceles the legs are equal length. Therefore the Pythagorean theorem can be written \[x^{2}+x^{2} = 8^{2}\] Solve for x.

Answer 3

since it's isosceles..the legs are equal..so a=b

a^2 + b^2 = c^2 is the pythagorean theorem

since a= b...it will become

a^2 + a^2 = c^2
2a^2 = c^2
a^2 = (c^2)/2
a = sqrt(c^2)/sqrt 2
so...
a = c/sqrt2
a = 8/sqrt 2

rationalize...

a = (8sqrt2)/2
a = 4sqrt2 = b