Question

ABC and XYZ are similar. Find the missing side length.

Answer 1

4

Explanation:

We have to find length of AC in ΔABC

Since ΔABC is similar to ΔXYZ, the corresponding sides of ΔABC to the corresponding sides of ΔXYZ should be of similar ratio

Equivalently stated

`(AB)/(XY) = (BC)/(YZ) = (AC)/(XZ)`

Plugging in known values we get

`(AB)/(XY) = (2)/(10) = (1)/(5)\\\\(BC)/(YZ) = (5)/(25) = (1)/(5)\\`

Thus we see that the length of each side of ΔABC is one-fifth the length of each corresponding side of ΔXYZ.

So

`AC =(1)/(5) XZ = (1)/(5) \cdot 20 = 4`

Answer 2

Hello there!

∆ABC and ∆XYZ are simular so:

`\displaystyle (AB)/(XY) = (BC)/(YZ) = (AC)/(XZ) \\ \\ (2)/(10) = (5)/(25) = (AC)/(20) \\ \\ (1)/(5) = (1)/(5) = (AC)/(20) \\ \\ (AC)/(20) = (1)/(5) \\ \\ AC = (20 * 1)/(5) = 4`

Answer: 4