A rectangle photograph is mounted on a square piece of cardboard whose sides have length x. the border that surrounds the photo is 3 inches on each side and 4 inches on both top and bottom
Let's say the length and width of the rectangle photograph are L and W, respectively.
The length of the cardboard is x, so the length of the rectangle photograph plus the two borders on the sides would be L + 2(3) inches.
Similarly, the width of the cardboard is x, so the width of the rectangle photograph plus the two borders on the top and bottom would be W + 2(4) inches.
We can set up an equation based on these relationships:
L + 2(3) = x
W + 2(4) = x
We can simplify these equations as:
L + 6 = x
W + 8 = x
To calculate the total outer dimensions of the photo, we add the length of the rectangle photograph plus the two side borders and the width of the rectangle photograph plus the two top and bottom borders:
Total length of the photo = L + 2(3) + L + 2(3) = 2L + 12 inches
Total width of the photo = W + 2(4) + W = 2W + 8 inches