Final answer:
The width of the photo is 12 cm and the length is 24 cm.
Step-by-step explanation:
To find the length of the photo, we need to set up an equation. Let's denote the width of the photo as 'x' cm. According to the problem, the photo is 12 cm longer than it is wide, so the length of the photo is 'x + 12' cm.
Now, we need to consider the frame. The frame is 3 cm wide on each side, so it adds a total of 6 cm to the width and length of the photo.
The total area of the frame is given as 468 cm². Since the frame is rectangular, we can calculate its area by multiplying its length by its width.
Therefore, we can set up the following equation to solve for the width of the photo:
x(x + 12) + 6(2x + 12) = 468
Simplifying the equation and solving for 'x', we get x = 12.
So, the width of the photo is 12 cm. Since the photo is 12 cm longer than it is wide, the length of the photo is 24 cm.