geometry
posted by HSutha .
The perimeter of right triangle RST is equal to the perimeter of isosceles triangle XYZ. The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isosceles triangle is an integer. what is the greatest possible length for one of the sides of isosceles triangle XYZ?

The hypotenuse of the right triangle is sqrt(6^2 + 8^2) = 10.
This makes the perimeter of RST 24.
Therefore, the maximum integer side of triangle XYZ is (24  2)/2 = 11.