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  • 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? 2-what are the dimensions of a rectangle with area 45m square. and the minimum perimeter?

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  1. anonymous
    • 5 years ago
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    Perimeter 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 = (40-2w)/2 = 20 - w Now substitute (20-w) in for L in Area formula ->A = (20-w)*w = 20w - w^2 Differentiate using power rule ->dA/dw = 20 - 2w set =0 and solve -> 20-2w = 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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