Question

If n ||m, find the value of x and the value of y.

A. y = 3.75, x = 11.25
B. y=4.x = 11
C. y = 5, x = 10
D. not enough information to determine

Answer 1

Answer: Option C

`y=5`,
`x=10`

Explanation:

If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' and c 'then:

`(a)/(a')=(b)/(b') =(c)/(c')`

In this case

`a = 12\\a' = 4\\c = 15\\c' = y`

So:

`(12)/(4)=(15)/(y)`

`3=(15)/(y)`

`y=(15)/(3)`

`y=5`

Therefore

if
`x+y=15` and
`y=5` then
`x =10`

Finally

`y=5`,
`x=10`