2005 PMWC Problems/Problem I12

Problem

In the figure below, $BCDE$ is a parallelogram, points $F$ and $G$ are on the segment $ED$ , $BCA$ is a right angled triangle, $AC$ is perpendicular to $BC$ .Suppose that $BC=8cm$ , $AC=7cm$ , and the area of the shaded regions is $12cm^2$ more than that of the triangle $AFG$ . What is the length of $CG$ ?

$[asy] fill((0,0)--(1,1)--(3,1)--(2,0)--cycle,grey); fill((0,0)--(2,1.5)--(2,0)--cycle,white); draw((0,0)--(2,1.5)--(2,0)--cycle,dot); draw((0,0)--(1,1)--(3,1)--(2,0)--cycle,dot); MP("B",(0,0),W);MP("A",(2,1.5),N);MP("C",(2,0),S); MP("E",(1,1),NW);MP("D",(3,1),NE); MP("F",(1.5,1),NW);MP("G",(2,1),NE); draw((1.9,0)--(1.9,.1)--(2,.1),linewidth(.75)); [/asy]$

Page

Toolbox

Search

2005 PMWC Problems/Problem I12

Problem

Solution

See Also