Question 355440
Let w = width of the rectangle, which is also the shortest side of the right triangle.  Then the other leg is w +2, and w+4 is the hypotenuse.  Then by the Pythagorean Theorem, {{{w^2 + (w+2)^2 = (w+4)^2}}},
{{{w^2+ w^2+4w+4 = w^2 +8w+16}}},
{{{w^2-4w-12 = 0}}},
{{{(w+2)(w-6) = 0}}}.
Thus w = 6, and the other leg is 8, and the hypotenuse is 10.