Current location - Health Preservation Learning Network - Slimming men and women - (2003? Guangzhou) has a rectangular land ABCDE with missing corners (as shown in the figure), in which AB= 1 10m, BC=80m, CD=90m, ∠ EDC = 135, and we need to use it now.
(2003? Guangzhou) has a rectangular land ABCDE with missing corners (as shown in the figure), in which AB= 1 10m, BC=80m, CD=90m, ∠ EDC = 135, and we need to use it now.
Solution: As shown in the figure, let DG⊥AB be in G, EF⊥BC be in F, DG, EF be in O, and let CN = X.

Then ∠ edo = ∠ EDC-90 = 45,

Therefore, △EOD is an isosceles right triangle. Similarly, △EQR and △RPD are also isosceles right triangles.

∴eo=od=ab-cd=20,rp=dp=cn=x,eq=qr=am=eo-rp=20-x,ae=bc-od=60,

If the area of the shaded portion MRNB is assumed to be y,

So y=MR? RN=(AE+QR)? (CD+RP)=(80-x)(x+90)= 7200- 10x-x2

Because y is a parabola with X opening downward and its symmetry axis is a straight line x=-5,

So when x≥0, the quadratic function is a decreasing function.

So the maximum value of this function is when x=0, y=7200,

So choose a.