SOLUTION: ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x. Show that the area 'y' of the quadrilateral CDFE is given by y = 1/

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x. Show that the area 'y' of the quadrilateral CDFE is given by y = 1/      Log On


   



Question 1012465: ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x.
Show that the area 'y' of the quadrilateral CDFE is given by y = 1/2 (1 + x - x^2). What is the quadrilaterals greatest possible area.

Answer by ikleyn(52848) About Me  (Show Source):
You can put this solution on YOUR website!
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ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x.
Show that the area 'y' of the quadrilateral CDFE is given by y = 1/2 (1 + x - x^2). What is the quadrilaterals greatest possible area.
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Hello,  I am slightly surprised.

In my opinion,  the area of the quadrilateral  CDFE  is   1 - x%5E2%2F2,  and it is not the same as your formula   y = 1/2 (1 + x - x^2).

For the proof that they are not the same,  I prepared this plot.



Figure. y = 1-x%5E2%2F2 (red) and y = 0.5%2A%281%2Bx-x%5E2%29 (green)