we can notice x is the sum of half DIA A and half BD
[tex]x=\frac{A}{2}+\frac{BD}{2}[/tex]and y is the sum of half DIA A and BD
[tex]y=\frac{A}{2}+BD[/tex]A. Find diameter A when x= 9..82 cm and y = 11.94 cm.
we replace x=9.8 and y=11.94 on the equations
[tex]\begin{gathered} 9.8=\frac{A}{2}+\frac{BD}{2} \\ \\ 11.94=\frac{A}{2}+BD \end{gathered}[/tex]now we have two equations and two unknows, then we can solve BD from the first equation
[tex]\begin{gathered} 9.8=\frac{A}{2}+\frac{BD}{2} \\ \\ 9.8-\frac{A}{2}=\frac{BD}{2} \\ \\ BD=19.6-A \end{gathered}[/tex]and replace on the second to find A
[tex]11.94=\frac{A}{2}+(19.6-A)[/tex]simplify
[tex]\begin{gathered} 11.94=\frac{A}{2}+19.6-A \\ \\ 11.94=-\frac{A}{2}+19.6 \end{gathered}[/tex]and solve for A
[tex]\begin{gathered} 11.94-19.6=-\frac{A}{2} \\ \\ -7.66=-\frac{A}{2} \\ \\ 7.66=\frac{A}{2} \\ \\ A=7.66\times2=15.32 \end{gathered}[/tex]Value of Diameter A is 15.32 cm
B. find y when diameter A = 30.36 cm and X =23.72 cm
now on the initial equations for x and y we replace A and X
[tex]\begin{gathered} 23.72=\frac{30.36}{2}+\frac{BD}{2} \\ \\ y=\frac{30.36}{2}+BD \end{gathered}[/tex]we have two equations, we realize we can simplify the first equation
[tex]\begin{gathered} 23.72=\frac{30.36}{2}+\frac{BD}{2} \\ \\ 23.72=15.18+\frac{BD}{2} \end{gathered}[/tex]and we can solve BD
[tex]\begin{gathered} 23.72-15.18=\frac{BD}{2} \\ 8.54=\frac{BD}{2} \\ \\ BD=8.54\times2=17.08 \end{gathered}[/tex]now we replace BD on the second equation
[tex]\begin{gathered} y=\frac{30.36}{2}+BD \\ \\ y=15.18+17.08 \\ \\ y=32.26 \end{gathered}[/tex]The value of y is 32.26 centimeters