Question

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?

Answer 1

Answer: w = 13 m, L = 19.5 m

Step-by-step explanation:

P = 3w + 2L

     3w + 2L = 78

              2L = 78 - 3w

                $L=\dfrac{78-3w}{2}$

                                       

A = w · L

$A=w\bigg(\dfrac{78-3w}{2}\bigg)\\\\\\A=\bigg(\dfrac{78w-3w^2}{2}\bigg)\\\\\\A=39w-\dfrac{3}{2}w^2\\\\\\0=-\dfrac{3}{2}w^2+39w-A$

    a=-3/2   b=39

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

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