Answer:
[tex]10\sqrt{2}[/tex]
Explanation:
There is a diagram attached which models the situation.
Since the given triangle is right, we are able to use the Pythagorean Theorem, which states when a and b are the legs of a right triangle and c is the hypotenuse:
[tex]a^{2} + b^{2} = c^{2}[/tex]
We can plug in the given values. Since both legs have a value of ten, we can say:
[tex]10^{2} + 10^{2} = c^{2}\\100 + 100 = c^{2}\\200 = c^{2}\\c = \sqrt{200}[/tex]
We can split 200 into 100 x 2, and [tex]\sqrt{100 }[/tex] is 10, so [tex]\sqrt{200} = 10\sqrt{2}[/tex]
Another way to do this use the given of the triangle being isosceles right. In an isosceles right triangle, the hypotenuse is always [tex]\sqrt{2}[/tex] times the base. So a triangle with legs 10 would have a hypotenuse of [tex]10\sqrt{2}[/tex].
