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.

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

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