In algebra, how do you find a frame thickness?

Question

How do you find the frame thickness of a picture frame that measures 17cm^2 by 19cm^2 if the area showing is equal to 137cm^2? I have been trying to work this and can not figure out what I am doing wrong.

I got to the point that 4x^2-72x+323=137 but can't get the answer to come out right. I keep getting 8.5cm as my answer. Anyone know?

Answer 1

(17 - 2x)(19 - 2x) = 137
323 - 72x + 4x^2 = -186
x^2 - 18x + 81 = 81 - 46.5
(x - 9)^2 = 34.5
x = 9 - √34.5
x = 3.12633 cm ≈ 3.125 cm