Question

Hallar el valor de x, e, y. En la figura. Ayuda porfavor.

Answer 1

`x=2.625\\ \\y=10`

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,

`(y)/(7.5)=(3.5)/(x)=(6)/(4.5)`

Now,

`(3.5)/(x)=(6)/(4.5)\\ \\6x=3.5\cdot 4.5\\ \\6x=15.75\\ \\x=2.625`

and

`(y)/(7.5)=(6)/(4.5)\\ \\4.5y=6\cdot 7.5\\ \\4.5y=45\\ \\y=10`