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
To find the area of the photograph, we need to subtract the area of the border from the area of the square. The area of the square is x^2.
The border has a width of 3 inches on each side, so the width of the rectangle is (x-6) inches.
The border has a height of 4 inches on the top and bottom, so the height of the rectangle is (x-8) inches.
Therefore, the area of the rectangle is (x-6)(x-8).
Checking the options:
- x^2: This represents the area of the square, which is not the area of the photograph.
- (x+8)(x+6): This does not represent the area of the photograph.
- (x-8)(x-6): This represents the area of the photograph.
- x^2+48: This represents the area of the square plus the area of the border, which is not the area of the photograph.
- x^2-48: This represents the area of the square minus the area of the border, which is not the area of the photograph.
- x^2+14x+48: This does not represent the area of the photograph.
- x^2-14x+48: This does not represent the area of the photograph.
Therefore, the expressions that represent the area of the photograph are (x-8)(x-6).