x is the unknown remaining edge of the base.
Using Pythagoras theorem in the base, we have:
[tex]8 {}^{2} + x {}^{2} = 10 {}^{2} [/tex]
[tex] = > \: x = \sqrt{10 {}^{2} - 8 {}^{2} } = 6[/tex]
with x = 6, the perimeter of the base is 10 + 8 + 6 = 24
