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Please answer this ASAP. Maribel is building rectangular pens for her dogs, as shown below. She will fence the entire rectangular area with 78m of fencing. What dimensions enclose the total maximum area. Show your work?

Please answer this ASAP. Maribel is building rectangular pens for her dogs, as shown-example-1
User Peter I
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1 Answer

5 votes

Answer: w = 13 m, L = 19.5 m

Explanation:

P = 3w + 2L

3w + 2L = 78

2L = 78 - 3w


L=(78-3w)/(2)

A = w · L


A=w\bigg((78-3w)/(2)\bigg)\\\\\\A=\bigg((78w-3w^2)/(2)\bigg)\\\\\\A=39w-(3)/(2)w^2\\\\\\0=-(3)/(2)w^2+39w-A

a=-3/2 b=39


\text{Axis of Symmetry}:w=(-b)/(2a)=(-39)/(2(-(3)/(2)))=(-39)/(-3)=\large\boxed{13}


\text{Maximum}:L=(78-3w)/(2)=(78-3(13))/(2)=(78-39)/(2)=(39)/(2)=\large\boxed{19.5}

User Kanak Sony
by
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