Question

An isosceles right triangle is a right triangle with congruent legs. If the length of each leg is represented by x, what algebraic expression can be used to represent the length of the hypotenuse?

Answer 1

Right triangle means Pythagorean theorem!
a^2+b^2=c^2
if each leg (a and b) = x, then
x^2+x^2=c^2
2x^2=c^2
solving for c by taking the square root of both sides leaves

c=x×sqrt(2)

c must be positive since its a length, so no need for a +- I. this case