We know line DE is parallel to line BC. Given the Area of ADE=9 and Area of CDE=6 , find the Area of ABC.

Guest Oct 22, 2018

#1**+1 **

Triangles ADE and DCE are under the same height....so....their areas are to each other as their bases.....so AD /DC = 9 / 6 = 3 / 2

So...AD / AC = 3 / 5

And triangles ADE and ABC are similar

So......the scale factor of AC / AD = 5/3

And the area of triangle ABC = [scale factor AC /AD]^2 * area of triangle ADE =

(5/3)^2 * 9 =

( 25 / 9 ) * 9 =

25 = [ ABC ]

CPhill
Oct 22, 2018