a2+b2=c2
x2+(x-2)2=102
x2+x2-4x+4=100
2x2-4x+4-100=0
2x2-4x-96=0
divide both sides by 2
x2-2x-48=0
factor
(x-8)(x+6)=0
x-8=0
x=8 inches
x-2=6 inches
x and x-2 are the legs and the hypotenuse is 10 inches
something I noticed...
are you familiar with a 3-4-5 right triangle ?
32+42=52, 9+16=25
if you double or triple or quadruple,or ...you get another right triangle
6,8,10 is a right triangle, 9,12,15 is a right triangle, etc
look at the 6-8-10 right triangle; the hypotenuse is 10 and one leg is 2 less than the other-exactly what was stated in the problem