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中4既數學問題 有１０點

發問:

http://x85.xanga.com/29ac306553232152578852/b113890195.jpg1 (a) Express EF in terms of x. (b) Express the area of rectangle BDEF in terms of x. (c) Find the dimensions and the area of the largest rectangle that can be inscribed in △ABC2 (a) Find the maximum area of the playground. (b) Find the... 顯示更多 http://x85.xanga.com/29ac306553232152578852/b113890195.jpg 1 (a) Express EF in terms of x. (b) Express the area of rectangle BDEF in terms of x. (c) Find the dimensions and the area of the largest rectangle that can be inscribed in △ABC 2 (a) Find the maximum area of the playground. (b) Find the dimensions of the rectangular playground if its area is a maximum. 更新: 1. in the figure, a rectangle BDEF of width x cm is inscribed in a right- angled triangle ABC, where AB=8 cm and BC = 12cm 第1題我唔明點解你直出答案,有冇式嫁? 2. Three sides of a rectangular playground are to be surrounded by a 60m fence.The remaining side is the entrance of playground

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最佳解答:

1) a) From your figure, In triangleABC, tan A=12/8=3/2 In triangleAFE, tan A=EF/AF=EF/(8-x) Hence, EF/(8-x)=3/2 ...................EF=3(8-x)/2 b) Area of BDEF= length*width=3x(8-x)/2 c) from b), Area=3x(8-x)/2 .......................=-3(x^2-8x)/2 .......................=[-3(x^2-8x+16)+48]/2 .......................=[-3(x-4)^2+48]/2 Hence, when x=4, it attains a max.area, and max. area is 24cm^2 Dimension of area = length*width ...........................= x*3(8-x)/2 hence, dimension of max. area = 4*6 2) Let x and y be the length and width of playground respectively. therefor, x+2y=60 Area of playground=xy ...........................=y(60-2y) ...........................=-2(y^2-30y) ...........................=-2(y^2-30y+225)+500 ...........................=-2(y-15)^2+500 hence, when y=15cm, it attains its max. of the area of playground; and max area of playround=500cm^2 c) Dimension = x*y ....................=(60-2y)*y Hence, Dimension of max area =30*15 cm 2007-10-18 14:28:56 補充： sorry for my typo.Area of playground should be-2(y^2-30y+225)+450=-2(y-15)^2+450Hence, max. area is 450m^2, not 500m^2

其他解答:

１： a) (8-x) tan(12/8) b) x(8-x) tan(4/3) c) A = x(8-x) tan(4/3) dA/dx= (8-2x)tan(4/3) max.Area =>>dA/dx=0 dA/dx= (8-2x)tan(4/3)=0 =>> x=4 =>> A=16 tan(4/3) ２：唔明7638E7481407D16B