Question

Triangles ABC and DEF are similar. 2.4 А E D 2 B 1. Find the length of segment DE: 2. Find the length of segment AC:

Answer 1

Let's begin by listing out the information given to us:

The 2 triangles are similar. This means that the ratio of the corresponding sides are equal

1.

`\begin{gathered} (|BC|)/(|EF|)=(|AB|)/(|DE|)\Rightarrow(4)/(2.4)=(2)/(|DE|) \\ (4)/(2.4)=(2)/(|DE|) \\ 4\cdot|DE|=2\cdot2.4\Rightarrow4\cdot|DE|=4.8 \\ 4\cdot|DE|=4.8 \\ |DE|=(4.8)/(4)=1.2 \\ |DE|=1.2 \end{gathered}`

2.

`\begin{gathered} (|BC|)/(|EF|)=(|AC|)/(|DF|)\Rightarrow(4)/(2.4)=(|AC|)/(3) \\ (4)/(2.4)=(|AC|)/(3) \\ 2.4\cdot|AC|=3\cdot4 \\ 2.4\cdot|AC|=12 \\ |AC|=(12)/(2.4)=5 \\ |AC|=5 \end{gathered}`