In feet, how far is it from third base across a baseball diamond to first base?

If I'm right in thinking that the distance the batter has to run from base to base is 90 feet, and that the diamond is a perfect square, then the distance from third base across to first in feet is the length of the hypotenuse of a right-angled triangle whose other two sides are 90 feet. So it's the square root of twice the square of 90, i.e. the sqaure root of 16,200 or 127.2792 (127 feet 3 inches and a bit).

But, being a Brit, I'm probably wrong about the length of a side of the diamond. I only know it's quite a bit more than a batsman has to run in cricket.

When location of home base is determined, with a steel tape measure 127 feet, 3 3/8 inches in desired direction to establish second base. From home base, measure 90 feet toward first base; from second base, measure 90 feet toward first base; the intersection of these lines establishes first base. From home base, measure 90 feet toward third base; from second base, measure 90 feet toward third base; the intersection of these lines establishes third base. The distance between first base and third base is 127 feet, 3 3/8 inches. All measurements from home base shall be taken from the point where the first and third base lines intersect.
http://www.baseball-almanac.com/rule1.shtml