The outside of a picture frame measures 8 in by 11 in 54in2 of the picture shows find the thickness of the frame?

Answer 1

To find the thickness of the frame, we start by determining the dimensions of the picture itself. The area of the picture is 54 in², and since the outside dimensions of the frame are 8 in by 11 in, we can set up the equation:

Let the thickness of the frame be ( x ). Then the dimensions of the picture are ( (8 - 2x) ) by ( (11 - 2x) ).

Setting up the equation:

[ (8 - 2x)(11 - 2x) = 54 ]

Expanding and simplifying gives us:

[ 88 - 22x - 16x + 4x^2 = 54 ] [ 4x^2 - 38x + 34 = 0 ]

Using the quadratic formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) with ( a = 4, b = -38, c = 34 ), we find ( x ). Solving this results in ( x \approx 1 ) inch. Thus, the thickness of the frame is approximately 1 inch.