Answer:
[tex]x=2.625\\ \\y=10[/tex]
Step-by-step explanation:
Thales theorem: If a straight line is drawn parallel to one of the sides of a triangle, then it cuts the other sides of the triangle, or these produced, proportionally; and, if the sides of the triangle, or the sides produced, are cut proportionally, then the line joining the points of section is parallel to the remaining side of the triangle.
Hence,
[tex]\dfrac{y}{7.5}=\dfrac{3.5}{x}=\dfrac{6}{4.5}[/tex]
Now,
[tex]\dfrac{3.5}{x}=\dfrac{6}{4.5}\\ \\6x=3.5\cdot 4.5\\ \\6x=15.75\\ \\x=2.625[/tex]
and
[tex]\dfrac{y}{7.5}=\dfrac{6}{4.5}\\ \\4.5y=6\cdot 7.5\\ \\4.5y=45\\ \\y=10[/tex]
