# Possible length of isosceles triangle side.

The perimeter of a right triangle $RST$ is equal to the perimeter of isoceles triangle $xyz$ The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isoceles triangle is an integer what is the greatest possible length for one of the sides of isoceles triangle $xyz$?

The hypotenuse of $RST$ is $\sqrt{100} = 10$

For $xyz$ let $xy = yz$ as the two equal legs, and $zx$ is the unequal, the "base" side.

Perimeter of $RST$ = $xyz$ = $24$

So leg $zx = 2$ is the lowest length the triangle can have, so that the other two are integers.

$xy + yz = 22 = 2xy \implies xy = 11 = yz$

Is this correct?