Question

DE is parallel to ACFind the lengths of AC and AD.

Answer 1

Since DE is parallel to AC the ratio between the sides of the triangles should be the same.

From the small triangle we notice that 4:5; from the big triangle we notice that 10:AC, since this ratios have to be equatl this means that:

`\begin{gathered} (4)/(5)=(10)/(AC) \\ AC=(10)/((4)/(5))=(50)/(4)=(25)/(2)=12.5 \end{gathered}`

Therefore, AC is 12.5 long.

To find AD we use the same principle. In the small triangle we have that 4:2; for the big triangle we have that 10:(2+AD). Then:

`\begin{gathered} (4)/(2)=(10)/(2+AD) \\ 2=(10)/(2+AD) \\ 2(2+AD)=10 \\ 2+AD=(10)/(2) \\ 2+AD=5 \\ AD=5-2 \\ AD=3 \end{gathered}`

Therefore, AD is 3 long.