Hey there! Let's solve this with a touch of humor, shall we?
To find x and y, we'll set up a system of equations using the given sides of the parallelogram.
Given:
Side 1: 2x + y = cm
Side 2: 3y - 2x = cm
Side 3: 5y - 8 = cm
Side 4: 4x - 3 = cm
Now, let's solve for x and y using these equations. Just bear with me, we're entering equation-solving territory!
Multiplying the first equation by 2:
4x + 2y = cm
Adding the second equation to this:
4x + 2y + (3y - 2x) = cm
2y + 3y = cm
5y = cm
y = (1/5)cm
Plugging the value of y back into the first equation:
2x + (1/5)cm = cm
2x = (4/5)cm
x = (2/5)cm
So, our thrilling conclusion is:
x = (2/5)cm
y = (1/5)cm
But wait, the fun doesn't end there! We still need to find the perimeter of this marvelous parallelogram.
Perimeter = 2 * (Side 1 + Side 2)
Perimeter = 2 * [(2x + y) + (3y - 2x)]
Perimeter = 2 * (2x + 3y)
Plugging in the values of x and y we found:
Perimeter = 2 * [(2 * (2/5)cm) + (3 * (1/5)cm)]
Perimeter = 2 * [(4/5)cm + (3/5)cm]
Perimeter = 2 * [(7/5)cm]
Perimeter = (14/5)cm
And there you have it! The perimeter of the parallelogram is (14/5) cm. I hope this answer brought a smile to your face, even if it's just a "geometry" smile!