Question

Among all rectangles that have a perimeter of 172 ,find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

Answer 1

We get that:

`\begin{gathered} A=l\cdot w \\ 2l+2w=172\rightarrow l+w=86\rightarrow l=86-w \end{gathered}`

so we get that the area is

`A=(86-w)w=86w-w^2`

so we get that the width of the rectangle with largest area is

`w=-(86)/(-2)=43`

and the length is

`l=86-43=43`

so the dimensions are 43 of length and 43 of width