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anonymous
 5 years ago
A. A rectangular garden with perimeter 40m is to be fenced.
1 What are dimensions of a garden and its maximum area?
2what are the dimensions of a rectangle with area 45m square. and the minimum perimeter?
anonymous
 5 years ago
A. A rectangular garden with perimeter 40m is to be fenced. 1 What are dimensions of a garden and its maximum area? 2what are the dimensions of a rectangle with area 45m square. and the minimum perimeter?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Perimeter of rectangle is 2L + 2w : where L,w are length and width Area is L*w ok so 2L + 2w = 40 and we need to maximize area This means define Area as a function of one variable, take derivative and set it equal to zero. Lets solve for L > L = (402w)/2 = 20  w Now substitute (20w) in for L in Area formula >A = (20w)*w = 20w  w^2 Differentiate using power rule >dA/dw = 20  2w set =0 and solve > 202w = 0 > 2w=20 > w =10 Now plug that value in for w in our perimeter formula and solve for L >2L + 2(10) = 40 > 2L = 20 > L = 10 So L=w=10 and area = 10*10=100 Hope this helps
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