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hello again everyone ><>< sorry but i need a bit more help
ABCD is a square of unit length and points Eand F are taken on the sides AB and AD respectively such that AE = AF = x
a) Express the area of the Quadrilateral CDFE as a function of x
b) Find the greatest area the quadrilateral can have
and if its not too much trouble can you please draw a diagram it would be most helpful
A square of unit length. Meaning, ABCD is 1 by 1.
Area of CDFE, K = (area of ABCD) minus (area of rigtht triangle EAF) minus (area of right triangle EBC)
K = 1*1 -[(1/2)(x)(x)] -[(1/2)(1-x)(1)]
K = 1 -(1/2)(x^2) -1/2 +(1/2)(x)
K = 1/2 +(1/2)(x) -(1/2)(x^2)
K = (1/2)(1 +x -x^2) ---------------the area of CDFE.
Greatest K is when dK/dx = 0, so,
dK/dx = (1/2)(1 -2x)
Set that to zero,
0 = 1 -2x
2x = 1
x = 1/2
Hence, greatest K = (1/2)[1 +1/2 -(1/2)^2] = (1/2)[1 +1/4] = 1/2 +1/8 = 5/8 sq.units ----answer.