10a=A; 7b=A; (a+10)^2+(a-10)^2=b^2 or 2a^2+200=b^2; 200=b^2-2a^2

Replace a and b with their A equivalents:

200=A^2(1/49-2/100) so, A=(200/(1/49-1/50))^.5, or A=(2*10*10*7*7*2*5*5)^.5=700.

Checking: a=70, b=100; 60^2+80^2=100^2, factor out 20^2 and you get the smallest Pythagorean right triangle. (I should have guessed!)