In a 45-45-90 triangle, the lengths of the legs are equal, and the relationship between the length of the legs (let's call it \( x \)) and the hypotenuse is given by the formula:
\[ \text{Hypotenuse} = x\sqrt{2} \]
Given that the hypotenuse is 10, we can set up the equation:
\[ 10 = x\sqrt{2} \]
To find the length of each leg (\( x \)), we can solve for \( x \):
\[ x = \frac{10}{\sqrt{2}} \]
To rationalize the denominator:
\[ x = \frac{10\sqrt{2}}{2} = 5\sqrt{2} \]
Thus, the length of each leg in the triangle is \( 5\sqrt{2} \).
The answer is 5√2.