Question

In the figure below, A ABC is similar to A XYZ. What is the length of ZX? Enter only the number as an integeror decimal.13N12351.25XBAThe solution is

Answer 1

ΔABC and ΔXYZ are similar triangles, then:

- The corresponding angles are equal

- The corresponding sides are at the same rate

You need to determine the length of ZX, so you have to work using the second property.

The corresponding sides are at the same ratio, this can be expressed as follows:

$\frac{XY}{BA}=\frac{YZ}{BC}=\frac{XZ}{AC}$

You can use

AC=13

ZX=N

BA=5

XY=1.25

$\begin{gathered} \frac{XY}{BA}=\frac{XZ}{AC} \\ \frac{1.25}{5}=\frac{N}{13} \end{gathered}$

Multiply both sides by 13:

$\begin{gathered} 13\cdot\frac{1.25}{5}=13\cdot\frac{N}{13} \\ 3.25=N \end{gathered}$

The length of ZX is 3.25 units.