Final answer:
The thickness of the frame can be determined by calculating the area of the full frame, deducting the area showing, and solving a quadratic equation involving the remaining dimensions.
Step-by-step explanation:
To find the thickness of a frame when the outside dimensions of the frame and the area of the visible picture are given, we can follow these steps:
- Calculate the area of the entire frame using the outside dimensions.
- Deduct the area of the visible picture from the area of the entire frame to get the area covered by the frame.
- Determine the uniform width of the frame, assuming it is the same on all sides and treat the frame as a border around the picture. This creates a smaller rectangle inside the larger one (representing the area of the visible picture).
- Use the formula for the area of a rectangle to express the dimensions of the inner rectangle. If the frame's thickness is x, then the dimensions of the inner rectangle would be (14 - 2x) by (20 - 2x).
- Set up the equation (14 - 2x)(20 - 2x) = 236, and solve for x, which is the frame's thickness.
For example, if the outside dimensions are 14 inches by 20 inches, and the area showing is 236 square inches:
- The area of the full frame would be 14 x 20 = 280 square inches.
- The area covered by the frame is 280 - 236 = 44 square inches.
- Solving for x would give us the thickness of the frame.
In this problem, we would solve the resulting quadratic equation to find that each side of the frame blocks off an equal width of the picture, which in turn tells us the frame's thickness.