Answer:
The length of XY is either 10 or 2.5.
Step-by-step explanation:
Given information: ZY = 5, XC = 3 and DC = 4.
Case 1: Rectangle ABCD is smaller than ZBXY.
The opposite sides of the rectangle are same.
[tex]ZY=BC+XC[/tex]
[tex]5=BC+3[/tex]
[tex]2=BC[/tex]
The length of ABCD is 4 and width of ABCD is 2. The width of ZBXY is 5. The corresponding sides of the similar rectangles are is in the same proportion.
[tex]\frac{4}{XY}=\frac{2}{5}[/tex]
[tex]\frac{4\times 5}{2}=XY[/tex]
[tex]10=XY[/tex]
Therefore the value of XY is 10.
Case 2: Rectangle ABCD is larger than ZBXY.
[tex]ZY=BC-XC[/tex]
[tex]5=BC-3[/tex]
[tex]8=BC[/tex]
The length of ABCD is 4 and width of ABCD is 8. The width of ZBXY is 5. The corresponding sides of the similar rectangles are is in the same proportion.
[tex]\frac{4}{XY}=\frac{8}{5}[/tex]
[tex]\frac{4\times 5}{8}=XY[/tex]
[tex]2.5=XY[/tex]
Therefore the value of XY is 2.5.
