L = length
w = width
r = diagonal, or hypotenuse
In order to solve this, you must use the Pythagorean theorem (a^2 + b^2 = c^2)
L = w + 9 = a
w = ? = b
r = 10 + w = c
Solve like so:
a^2 + b^2 = c^2
(w + 9)^2 + w^2 = (10 + w)^2
(w + 9)(w + 9) + w^2 = (10 + w)(10 +w)
w^2 + 18w + 81 + w^2 = w^2 + 20w + 100
2w^2 + 18w + 81 = w^2 + 20w + 100
w^2 + 18w + 81 = 20w + 100
w^2 + 81 = 2w + 100
w^2 - 19 = 2w
2 = w - 19/w
w = 2 + 19/w
w ends up being equal to 5.47 as a decimal answer. The work to solve this equation further would require me to spend another couple hours to present. So if you wish to see how this is done, go to quickmath.com.
