a - the leg lengths
h - the hypotenuse length
We use the Pythagorean theorem:
[tex] h^2=a^2+a^2\\\\h^2=2a^2\to h=\sqrt{2a^2}\\\\h=\sqrt2\cdot\sqrt{a^2}\\\\h=a\sqrt2 [/tex]
Substitute the value of h = 10:
[tex]a\sqrt2=10\ \ \ |\cdot\sqrt2\\\\2a=10\sqrt2\ \ \ |:2\\\\a=5\sqrt2[/tex]
Answer: 5sqrt(2)
