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.
the following expressions represent the area of the photograph? check all that apply
x^2
(x+8)(x+6)
(x-8)(x-6)
x^2+48
x^2-48
x^2+14x+48
x^2-14x+48
The area of the photograph is equal to the area of the cardboard minus the area of the borders surrounding the photograph.
The area of the cardboard is given by the expression x^2.
The area of the borders is equal to 3 inches on each side plus 4 inches on both top and bottom, which gives a total border width of 3+3+4+4=14 inches.
So, the expression for the area of the photograph is x^2 - 14 inches.
Out of the given expressions:
- x^2 is the area of the photograph without the borders, so it is a valid expression for the area of the photograph.
- (x+8)(x+6) is not a valid expression for the area of the photograph, as it represents the area of the cardboard with borders included.
- (x-8)(x-6) is not a valid expression for the area of the photograph, as it represents the area of the cardboard with borders excluded.
- x^2+48 represents the area of the cardboard with borders included, so it is not a valid expression for the area of the photograph.
- x^2-48 represents the area of the cardboard with borders excluded, so it is not a valid expression for the area of the photograph.
- x^2+14x+48 represents the area of the cardboard with borders included, so it is not a valid expression for the area of the photograph.
- x^2-14x+48 represents the area of the cardboard with borders excluded, so it is not a valid expression for the area of the photograph.
Therefore, the valid expressions for the area of the photograph are x^2.