There is this specific ratio for 45-45-90 triangles where the length of the hypotenuse is radical 2 times as long as a leg. With this in mind, we can create an equation where the length of one leg is represented with the variable x.
x[tex] \sqrt{2} [/tex] = 10[tex] \sqrt{5} [/tex]
divide both sides by [tex] \sqrt{2} [/tex]
x = 10[tex] \sqrt{5} [/tex] / [tex] \sqrt{2} [/tex]
x = 10[tex] \sqrt{10} [/tex] /2
x = 5[tex] \sqrt{10} [/tex]
The length of one leg is 5[tex] \sqrt{10} [/tex]
