A square-shaped canvas painting was enlarged by adding a 4-centimeter wide decorative frame to the length and width of the canvas. If the area of the framed painting is 625 square centimeters, what is the side length of the bare canvas?

1. Let the side length of the bare canvas be \(x\) centimeters.
2. The frame adds 4 centimeters to each side, so the total side length of the framed painting is \(x + 8\) centimeters.
3. The area of the framed painting is given as 625 square centimeters.
   Set up the equation for the area:
   \[( x + 8) ^ 2 = 625\]
4. Solve for \(x\):
   \[x + 8 = \sqrt { 625} \]
   \[x + 8 = 25\]
   \[x = 25 - 8\]
   \[x = 17\]

Therefore, the side length of the bare canvas is 17 centimeters.

Supplemental Knowledge

Understanding geometric shapes - especially squares - such as their area calculations and how changes affect dimensions is of vital importance when working with these objects.
For a square:

• The area is calculated as the side length squared (\(\text { side} ^ 2\)).
• If you add a frame around the square, you increase both the length and width by twice the frame's width. This is because the frame adds to both sides of each dimension.

Applied Knowledge

Imagine you have a square photo and you decide to put it in a decorative frame. If the frame adds 4 cm to each side, this means:

• The original photo size increases by 8 cm in total (4 cm on each side).
  For example:
• If your original photo was 10 cm by 10 cm, adding a 4 cm frame would make it \(( 10 + 8) \times ( 10 + 8) = 18 \times 18\).

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