A picture frame has a total perimeter of 2 meters. The height of the frame is 0.62 times its width.
(a) Write the height in terms of the width and write an equation for the perimeter in terms of the width.
I know that the height would be h=0.62w
but I don't know how to set up the perimeter. I think it goes something like p=_w. So, could you help out with figuring out what goes there in the blank.
Oh, I love putting frames around things! Let's frame this problem together.
We know that the perimeter of a rectangle is the sum of all its sides. In this case, we have two sides of width 'w' and two sides of height 'h.'
So, the perimeter of the picture frame (p) can be expressed as:
p = 2w + 2h
Since the height (h) is 0.62 times the width (w), we can substitute h with 0.62w:
p = 2w + 2(0.62w)
Simplifying, we get:
p = 2w + 1.24w
Combining like terms, we find:
p = 3.24w
So, the equation for the perimeter (p) in terms of the width (w) is p = 3.24w.
Now, we got our frame! Time to put something funny in it.
To find the perimeter, we need to consider all sides of the picture frame. Since a picture frame typically has four sides, let's denote the width of the frame as "w".
The height of the frame is given as 0.62 times its width, so we can write the height as:
h = 0.62w.
The perimeter of the frame is the sum of the lengths of all four sides. In this case, we have two sides with length "w" (top and bottom), and two sides with length "h" (left and right).
Therefore, the equation for the perimeter can be written as:
Perimeter = 2w + 2h.
Substituting the value of height we found earlier:
Perimeter = 2w + 2(0.62w).
Simplifying further:
Perimeter = 2w + 1.24w.
Perimeter = 3.24w.
In general, the equation for the perimeter in terms of the width "w" is:
Perimeter = 3.24w.
To find the perimeter of the picture frame, we need to add up the lengths of all four sides. Let's consider the sides of the frame:
1. The top side has the same length as the width, which we'll call "w."
2. The bottom side also has the same length as the width, "w."
3. The left side is the height, which we'll call "h."
4. The right side is also the height, "h."
Now, let's add up the lengths of the sides to find the perimeter:
Perimeter = length of top side + length of bottom side + length of left side + length of right side
Perimeter = w + w + h + h
Since the height (h) is 0.62 times the width (w), we can write the equation for the perimeter in terms of the width:
Perimeter = w + w + 0.62w + 0.62w
Simplifying the equation, we have:
Perimeter = 2w + 1.24w
Perimeter = 3.24w
to go around the frame, which is what the perimeter is, you will need two widths and two heights.
so..
2w + 2h = 2
or
w + h = 1 by dividing by 2
but h = .62w
so w + .62 w = 1
1.62w = 1
solve for w