umm The perimeter of the rectangle below is 64 units. Find the length of side xy .
_x____?_____y_
/ /
3x/ /
/_v____2x+2____w_/
yaa so thats the rectangle lol
Help plz..
it appears that 2(3x + 2x+2) = 64
x = 12
so the rectangle is 36 by 26
To find the length of side xy, we need to use the information provided about the perimeter of the rectangle.
The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, we are given that the perimeter is 64 units.
Using the given information about the rectangle's sides, we can set up an equation to solve for the length of xy.
The lengths of the sides are as follows:
Side xw: 3x
Side wx: 2x + 2
Side yw: 3x (since it is parallel to xw)
The length of side xy is equal to the sum of xw and wx:
xy = xw + wx
xy = 3x + (2x + 2)
xy = 5x + 2
Now, since we know that the perimeter of the rectangle is 64 units, we can set up an equation:
Perimeter = 2(xw + wx + yw + xy)
Plugging in the lengths of the sides, we get:
64 = 2(3x + 2x + 2 + 3x + 5x + 2)
Simplifying the equation, we have:
64 = 2(13x + 4)
64 = 26x + 8
56 = 26x
Dividing both sides of the equation by 26, we find:
x = 2
Now that we know the value of x, we can find the length of side xy:
xy = 5x + 2
xy = 5(2) + 2
xy = 10 + 2
xy = 12
Therefore, the length of side xy is 12 units.
To find the length of side xy, we need to solve for the value of x. We are given that the perimeter of the rectangle is 64 units.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Let's start by finding the length of the rectangle. Looking at the diagram, we can see that the length is equal to the segment xy + segment w. Hence, the length can be expressed as (xy + w).
Similarly, the width of the rectangle can be calculated as the sum of segment x + segment 3x. So, the width can be expressed as (x + 3x) or 4x.
Now, using the formula for the perimeter:
64 = 2[(xy + w) + (4x)]
Simplify the equation:
64 = 2(xy + w + 4x)
Divide both sides of the equation by 2:
32 = xy + w + 4x
Next, let's substitute the given values:
32 = xy + (2x + 2) + 4x
Simplify further:
32 = xy + 2x + 2 + 4x
Combine like terms:
32 = xy + 6x + 2
Rearrange the equation to make it easier to solve:
xy + 6x = 30
Now, we need more information or another equation to solve for the value of xy.