A rectangular painting measures 1212 inches by 1414 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 7676 inches. Determine the width of the frame.

Answer: the width of the frame is 303 inches.

Step-by-step explanation:

Let x represent the width of the frame.

The rectangular painting measures 1212 inches by 1414 inches and contains a frame of uniform width around the four edges. This means that the length of the painting and the frame is 1212 + 2x and the width of the painting and the frame is 1414 + 2x

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2 (length + width)

The perimeter of the rectangle formed by the painting and its frame is 7676 inches. This means that

2 (1212 + 2x + 1414 + 2x) = 7676

2 (2626 + 4x) = 7676

Dividing through by 2, it becomes

2626 + 4x = 7676/2 = 3838

4x = 3838 - 2626 = 1212

x = 1212/4 = 303 inches

The answer to your question is 303 in

Step-by-step explanation:

Data

Painting 1212 in x 1414 in

Perimeter painting + frame = 7676

width of the frame = ?

Process

1. - Calculate the perimeter of the painting

Perimeter = 2 length + 2 width

Perimeter = 2 (1212) + 2 (1414)

Perimeter = 2424 + 2828

Perimeter = 5252 in

2. - Subtract both perimeters

7676 - 5252 = 2424 in

3. - Divide the result by 8 because there are 8 borders

2424/8 = 303 in

4. - Conclusion

The frame has a width of 303 in