Question

The outside of a picture frame measures 14 in and 20 in 196in^2 of the picture shows find the thickness of the frame

Answer 1

The described picture frame can be visualized into two separate parts. The first area is equal to the area using the outermost dimensions for the length and width. 
             Area = Length x Height
              Area = (20 in) x (14 in) 
              Area = 280 in²

We are given that the area is only equal to 192 in². We subtract this value from the computed area.
         Difference = 280 in² - 192 in²
               difference = 88 in²

This area is equal to the area of the hollow space inside the frame. That is equal to,
      height = 20 in - 2x
      length = 14 in - 2x

The area,
               88 = (20 - 2x)(14 - 2x)

Simplify the right hand side of the equation.
             88 = 280 - 68x + 4x²

Divide the equation by 4,
            22 = 70 - 17x + x²

Transposing,
                x² - 17x - 48 = 0
The factors of the equation is 58.2. 

Thus, the thickenss is equal to 58.2 in