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 CDEF is given by y = 1/
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-> 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 CDEF is given by y = 1/
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Question 1012602: 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 CDEF is given by y = 1/2 (1 + x - x^2). What is the quadrilaterals greatest possible area. Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! area of triangle EAF = x^2 / 2
area of triangle EBC = ((1-x)*1) / 2 = (1-x) / 2
area of square ABCD = 1 * 1 = 1
area of quadrilateral CDEF(y) = area of square ABCD - area of triangle EAF - area of triangle EBC
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y = 1 - x^2/2 - (1-x) / 2
y = (2 - x^2 - (1-x)) / 2
y = (1 +x -x^2) / 2
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this is a parabola that opens downward, so we want the value of x at the parabola's peak.
x = -b / 2a = (-1/2) / (2 * (-1/2)) = 1/2
now substitute 1/2 for x in the equation for y
y = (1 +(1/2) - (1/2)^2) / 2 = (5/4) / 2 = 5/8
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the greatest possible area for quadrilateral CDEF is 5/8
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here is the graph of the area of quadrilateral CDEF
