Let’s denote the length of XA as x and the length of CY as y.
The area of a parallelogram is given by the formula: Area = base * height.
In this case, the base of the parallelogram is AB, and the height is AX. So, we have:
45/4 = AB * AX
Similarly, the base of the parallelogram is CD, and the height is CY. So, we have:
45/4 = CD * CY
Since AB = CD (opposite sides of a parallelogram are equal in length), we can equate the two equations:
AB * AX = CD * CY
Since AB = CD, we can simplify the equation to:
AB * AX = AB * CY
Dividing both sides by AB, we get:
AX = CY
So, the lengths of XA and CY are equal.
Since the area of the parallelogram is given as 45/4 cm², we can substitute this value into the equation for the area:
45/4 = AB * AX
Since AX = CY, we can substitute CY for AX:
45/4 = AB * CY
Now, we need to find the value of AB. To do this, we can use the fact that the area of a parallelogram is also given by the formula: Area = base * height.
In this case, the base is AB and the height is CY. So, we have:
45/4 = AB * CY
Since AX = CY, we can substitute AX for CY:
45/4 = AB * AX
Now, we have two equations:
45/4 = AB * AX 45/4 = AB * AX
Since the lengths of XA and CY are equal, we can solve for AB and AX simultaneously.
Dividing both sides of the first equation by AX, we get:
45/4AX = AB
Substituting this value of AB into the second equation, we get:
45/4 = (45/4AX) * AX
Simplifying, we get:
45/4 = 45/4
This equation is true for any value of AX. Therefore, the lengths of XA and CY can be any value as long as they are equal.
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