In the above figure, $AB = 12$, $FE = 8$, $BC = CD = DE = 3$, $AB\perp BE$, $FE\perp BE$,
Then find the area of $\Delta GCD$.
+130071 If we draw perpendicular GM to BE then we form two triangles
Triangle GMD is similar to triangle ABD ....and triangle FEC is similar to triangle GMC
So And
AB/ BD = GM / x FE / CE = GM/ 3 -x
12/6 = GM /x 8 / 6 = GM / 3 - x
2 = GM / x 4 / 3 = 2x / 3 - x cross- multiply
GM = 2x 4(3 -x) = 3 * 2x
12 - 4x = 6x
12 = 10x
x =12/10 = 6/5
So GM = 2 (6/5) = 12/5
So [ GCD ] = 1/2 ( CD) ( GM) = 1/2 ( 3) (12/5) = 36/10 = 3.6
