Solution
Given the similar triangles
The proportion/ratio of the similar triangles are
[tex]\frac{12}{16}=\frac{6}{x}=\frac{8}{y}[/tex]
To find the values of x and y, take into consideration the given propotion i.e
[tex]\begin{gathered} \frac{12}{16}=\frac{6}{x} \\ \text{Crossmultiply} \\ 12x=96 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{96}{12} \\ x=8 \end{gathered}[/tex]
Hence, the value of x is 8.
For the value of y
[tex]\begin{gathered} \frac{12}{16}=\frac{8}{y} \\ \text{Crossmultiply} \\ 12y=128 \\ \text{Divide both sides by 12} \\ \frac{12y}{12}=\frac{128}{12} \\ y=\frac{32}{3} \end{gathered}[/tex]
Hence, the value of y is 32/3
Thus the value of x = 8 and y = 32/3
