Question

The ratio of Bf to Be is 1 to 4. If the area of triangle ABC is 12 and the area of triangle AFD is 6, what is the ratio of side AD to side AC.

Answer 1

\[\frac{BF}{BE}=\frac{1}{4}\] or \(BE=4\times BF~~~(1)\) where BE and BF are heights of given triangles in the problem...

...the area for the triangle is \[Area_\triangle=\frac{1}{2}base \times height\]
\[A_{\triangle ABC}=\frac{1}{2} AC \times BE=12~~~(2)\]
\[A_{\triangle AFD}=\frac{1}{2} AD \times BF=6~~~(3)\]...using the derived equations, you can determine the ratio of side AD to side AC... solve (2) and (3) to solve AC and AD respectively, plug-in (1) to (2) and get the ratio AD/AC... you can continue up to this point...

Answer 2

Ty