Final answer:
To find the width of the frame around the picture, subtract the area of the picture from the area of the outside of the frame and divide by the length of one side of the frame. In this case, the width of the frame is approximately 2.68 cm.
Step-by-step explanation:
To find the width of the frame around the picture, we need to subtract the area of the picture from the area of the outside of the frame. The outside area of the frame can be calculated by multiplying the length and width of the frame, while the area of the picture can be calculated by multiplying its length and width. By subtracting the area of the picture from the area of the frame, we can determine the area of the frame. Since the frame has a uniform width on all sides, we can calculate its width by dividing the frame area by the length of one side of the frame. In this case, the frame width would be the square root of the frame area.
Let's calculate:
Outside area of the frame = Length x Width
Area of the picture = 260 cm²
Frame area = Outside area of the frame - Area of the picture
Width of the frame = √(Frame area) / Length of one side of the frame
Substituting the given values:
Outside length = 14 cm
Outside width = 30 cm
Outside area of the frame = 14 cm x 30 cm = 420 cm²
Frame area = 420 cm² - 260 cm² = 160 cm²
Width of the frame = √(160 cm²) / 30 cm ≈ 2.68 cm
Therefore, the width of the frame around the picture is approximately 2.68 cm.