ABCD is a square with point E on BC. DEFG is a rectangle with point A on FG.
Let x=CE. Express area(ABCD)/area(DEFG) in terms of x.
When x=CD=0, the areas are obviously equal and the ratio is 1.
When x=CD=CB, a little bit of arithmetic shows the ratio is either also 1, as the rectangle has sides equal to sqrt(2) times the side of the square and the side of the square divided by sqrt(2).
In between, Geometers Sketchpad indicates the same holds for intervening values of x. That is, the ratio is 1 regardless of x.
|
|
Posted by Charlie
on 2019-07-04 14:37:07 |
GSP solution
