Given parallelogram ABCD, find the values of x and y.
AX = y + 4
XC = 2y - 8
DX = x + 5
XB = 3x
To find the values of x and y in the parallelogram ABCD, we need to use the properties of a parallelogram.
Since opposite sides of a parallelogram are equal in length, we can set up two equations using the given side lengths:
AX = XC (opposite sides)
y + 4 = 2y - 8
And
XB = DX (opposite sides)
3x = x + 5
Now, let's solve each equation one at a time:
1. y + 4 = 2y - 8
First, simplify the equation by subtracting y from both sides:
4 = y - 8
Next, add 8 to both sides of the equation:
4 + 8 = y
y = 12
So, the value of y is 12.
2. 3x = x + 5
First, subtract x from both sides of the equation:
3x - x = 5
Simplify the equation:
2x = 5
Finally, divide both sides of the equation by 2:
x = 5/2
So, the value of x is 5/2 or 2.5.
Therefore, the values of x and y in parallelogram ABCD are x = 2.5 and y = 12.