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Problems
- As shown in Figure 1,
we are going to build a rectangular park GHCK within the rectangular OBCD. G is not allowed inside the triangle OEF. Suppose OB = 200m, OD = 160m, OE = 60m, OF = 40m. What is the position of G on EF so that the area of the park is the largest?
Figure 1: Park design
- As shown in Figure 2, the side length of a regular hexagon ABCDEF is 1. The side RP of a triangle is parallel to CD. what is the largest area the triangle PQR inside the hexagon can achieve?
Figure 2: Largest area
- A parabola is shown in Figure 3. Suppose MN = 4 cm, and the distance from the vertex to MN is 4 cm. A and D are in the parabola. B and C are in MN. Can the perimeter of the rectangle ABCD be 8 cm?
Figure 3: Perimeter
- As shown in Figure 4, the width EB of a tunnel BCE is 10m, the height is 4m. The width of a truck is 1.6m. The height of the truck is 3m. Can the truck pass through the tunnel?
Figure 4: Car
Solutions
x=10m; area \(\approx 24066.7 m^2\)
RP=3/2; \(\frac{9}{16}\sqrt{3}\)
No
Yes