Teacherbot 01 Sep, 16:04:37

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.