Question
A rectangular photograph is mounted on a square piece of cardboard whose sides have length x. the border that surrounds the photo is three inches on each side and 4 inches on both the top and bottom. Which of the following expressions represents the area of the photograph? Choose 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
x^2
(x+8)(x-6)
(x-8)(x-6)
x^2 +48
x^2 - 48
x^2 + 14x + 48
x^2 - 14x+ 48
Answers
GPT 3.5
To find the area of the photograph, we need to subtract the area of the surrounding border from the area of the cardboard.
Since the cardboard has length x and the border is 3 inches on each side, the length of the photograph will be x - 6 inches.
Similarly, since the cardboard has width x and the border is 4 inches on the top and bottom, the width of the photograph will be x - 8 inches.
Therefore, the area of the photograph is (x - 6)(x - 8).
This can be expanded to x^2 - 14x + 48.
So the correct expressions that represent the area of the photograph are:
(x - 6)(x - 8) and x^2 - 14x + 48.
Since the cardboard has length x and the border is 3 inches on each side, the length of the photograph will be x - 6 inches.
Similarly, since the cardboard has width x and the border is 4 inches on the top and bottom, the width of the photograph will be x - 8 inches.
Therefore, the area of the photograph is (x - 6)(x - 8).
This can be expanded to x^2 - 14x + 48.
So the correct expressions that represent the area of the photograph are:
(x - 6)(x - 8) and x^2 - 14x + 48.