Question

△ XYZ∼ △ DEF, YZ is 10 meters, ​ XZ ​ is 15 meters, and EF is 8 meters. What is ​ DF?

Answer 1

im not for sure on this but i would say DF is 13

Answer 2

△ XYZ∼ △ DEF, YZ is 10 meters, ​ XZ ​ is 15 meters, and EF is 8 meters. What is ​ DF?

Solution:

As, △ XYZ∼ △ DEF , so the ratio of sides of triangle is equal.

So, we have,
`(XY)/(DE) =(YZ)/(EF) =(XZ)/(DF)`

Using,
`(YZ)/(EF) =(XZ)/(DF)`

So, we get,
`(10)/(8) =(15)/(DF)`

Now, to solve for DF, we must simplify

Simplifying,

`(5)/(4) =(15)/(DF)`

To simplify, Let us multiply by 4*DF on both sides

`(5*4DF)/(4) =(15*4DF)/(DF)`

`(5DF)/(1) =(15*4)/(1)`

So, 5 DF=15*4=60

To solve for DF, let us divide by 5 on both sides

`(5)/(5) DF=(60)/(5)`

`(1)/(1) DF=(12)/(1)`

So, DF=12meters