Question

TU || VX. Find UV.

63
45
15
V
W
T
X

Answer 1

UV = 21

Explanation:

Given a line parallel to a side of a triangle , that is VX is parallel to TU, and it intersects the other two sides, then it divides those sides proportionally, so

`(WV)/(UV)` =
`(WX)/(TX)` =
`(45-15)/(15)` =
`(30)/(15)` = 2 , that is

`(WV)/(UV)` = 2

Now, WV = 63 - UV

substituting into the ratio , gives

`(63- UV)/(UV)` = 2 ( multiply both sides by UV )

2 UV = 63 - UV ( add UV to both sides )

3 UV = 63 ( divide both sides by 3 )

UV = 21