Question 343299
Please Help Me with this question!

The Length of one leg of an isosceles right triangle is 6 inches. Express the length of the hypotenuse in simplest radical form.


Since this triangle is a right triangle, the legs will have the same measure, and since one leg is 6 inches, then the other is 6 inches also.


Now, using the pythagorean formula, {{{c^2 = a^2 + b^2}}}, with "c" being the length of the hypotenuse, and both "a" and "b" the legs,we get: 

{{{c^2 = 6^2 + 6^2}}} 

{{{c^2 = 36 + 36}}}

{{{c^2 = 72}}}

{{{c = 0 +- sqrt(72)}}}_____Taking the square root of each side of equation in order to isolate c, the hypotenuse


{{{c = sqrt(72)}}}______Ignoring the negative value as measurements CAN NOT be  expressed with negatives values

{{{c = sqrt(36*2)}}}_______{{{c = sqrt(36)*sqrt(2)}}}

c, or hypotenuse = {{{highlight_green(6sqrt(2))}}}