Question

How do I find out the two missing lengths

Answer 1

x=
`10(10)/(7)` and y= 10.

Explanation:

It is given that the triangles are similar.

So, the ratio of their sides will be equal.

i.e.
`(21)/(14)=(16)/(x)=(15)/(y)`

i.e.
`(3)/(2)=(16)/(x)=(15)/(y)`

This gives us that,

`(3)/(2)=(16)/(x)` and
`(3)/(2)=(15)/(y)`

i.e.
`x=(16* 2)/(3)` and
`y=(15* 2)/(3)`

i.e.
`x=(32)/(3)` and
`y=(30)/(3)`

i.e. x= 10.7=
`10(10)/(7)` and y= 10

Thus, the side lengths are x=
`10(10)/(7)` and y= 10.