Answer:
XY = 30 units
Explanation:
The formula for the perimeter of a rectangle is given by:
P = 2l + 2w, where
- P is the perimeter,
- l is the length,
- and w is the width.
Since the opposite sides of rectangles are equal, WV = XY and VY = WX.
Thus, the length of side XY is also 3y + 3, and the length of side WX is also 2y + 2.
Note that sides VY and WX represent the width of the rectangle while sides WV and XY represent the length of the rectangle.
Step 1: Find y:
Before we can find the length of side XY, we'll first need to know the value of the variable y in 3y + 3 and 2y + 2.
We can find y by plugging in 3y + 3 for l and 2y + 2 for w, and 100 for P in the perimeter formula:
100 = 2(3y + 3) + 2(2y + 2)
100 = (2 * 3y) + (2 * 3) + (2 * 2y) + (2 * 2)
100 = (6y + 4y) + (6 + 4)
(100 = 10y + 10) - 10
(90 = 10y) / 10
9 = y
Thus, y = 9.
Step 2: Find the length of side XY:
Now we can find the length of side XY by plugging in 9 for y in 3y + 3 and simplifying:
XY = 3(9) + 3
XY = 27 + 3
XY = 30
Thus, the length of side XY is 30 units.