Question

The outside of a picture frame measures 14 in. by 18 in., and 96 in^(2) of the picture shows. Find the thickness of the frame

Answer 1

The thickness of the picture frame is 1.5 inches.

Step-by-step explanation:

To find the thickness of the picture frame, we can use the given information about the dimensions of the outer frame and the area of the picture. The frame has dimensions 14 inches by 18 inches, and the area of the picture showing is 96 square inches.

Let's denote the thickness of the frame as
`\( t \)`. The dimensions of the inner picture (excluding the frame) can be calculated by subtracting twice the thickness from the length and width of the outer frame. Therefore, the inner dimensions are
`\( (14 - 2t) \)` inches by
`\( (18 - 2t) \)`inches.

The area of the inner picture is then given by the product of its length and width:
`\((14 - 2t) * (18 - 2t)\)`. Since the area of the picture is 96 square inches, we can set up the equation
`\((14 - 2t) * (18 - 2t) = 96\)` and solve for
`\( t \).`

By solving the quadratic equation, we find that the thickness of the frame
`(\( t \))` is 1.5 inches. This solution ensures that the inner picture dimensions and the frame dimensions together satisfy the given conditions. Therefore, the thickness of the picture frame is 1.5 inches.