Question

Find DE in the diagram shown. Write your answeras a decimal rounded to the nearest tenth.

Answer 1

DE = 7.9

Step-by-step explanation

As shown in the diagram, these two triangles are similar by the AA postulate. The corresponding sides are: AC-DF, AB-DE, BC-EF.

In similar triangles, the ratio between corresponding sides must be constant:

`(AB)/(DE)=(BC)/(EF)`

Replacing with the measures we know we can solve for DE:

`\begin{gathered} (11)/(DE)=(14)/(10) \\ DE=11\cdot(10)/(14) \\ DE\approx7.9 \end{gathered}`