A large picture,2m by 2m,is displayed on a wall.It is place in a frame with a border of uniform width.
A. How would you represent the length of side of the frame?
B. What expression represent the area of the frame?
see your previous post of this question. What do you not understand about what I said there?
Can you please answer my question.
ok. the picture has length 2 and width 2
There is a frame of width w all around. So, now the length is w+2+w and the width is w+2+w, or 2+2w
So, the area (which I am sure you know is length * width) is just
(2+2w)(2+2w) = (2+2w)^2 = 4(w+1)^2
Are you sure?
A. To represent the length of a side of the frame, you need to consider that the frame has a uniform width. Let's denote this width as "w". In this case, the frame will add "w" to both the length and width of the picture. Therefore, the length of a side of the frame can be represented as "2m + 2w".
B. To find the expression that represents the area of the frame, you need to subtract the area of the picture from the area of the frame including the picture. The area of the frame including the picture is given by the length of one side of the frame multiplied by the length of the other side of the frame. So, the area of the frame (A_frame) is:
A_frame = (2m + 2w) * (2m + 2w)
To get the expression that represents only the area of the frame without the picture, you need to subtract the area of the picture (A_picture) from A_frame:
Expression for the area of the frame = A_frame - A_picture