Question

In the figure below, is similar to . What is the length of ? Enter only the number as an integer or decimal.

Answer 1

Given that,

`\Delta ABC\cong\Delta XYZ`

To solve for the length of the side XZ, we will apply the method of similar triangles.

Therefore,

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

Given data,

`\begin{gathered} AB=2 \\ AC=3 \\ XY=7 \\ XZ=\text{?} \end{gathered}`

Let us now substitute the given data and solve for the length XZ,

`\begin{gathered} (2)/(3)=(7)/(XZ) \\ \text{cross multiply,} \\ 2XZ=3*7 \end{gathered}`

`\begin{gathered} 2XZ=21 \\ \text{divide both sides by 2,} \\ (2XZ)/(2)=(21)/(2) \\ XZ=10.5 \end{gathered}`

Hence, the length of ZX is 10.5.