contestada

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.

Respuesta :

We get that:

[tex]\begin{gathered} A=l\cdot w \\ 2l+2w=172\rightarrow l+w=86\rightarrow l=86-w \end{gathered}[/tex]

so we get that the area is

[tex]A=(86-w)w=86w-w^2[/tex]

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

[tex]w=-\frac{86}{-2}=43[/tex]

and the length is

[tex]l=86-43=43[/tex]

so the dimensions are 43 of length and 43 of width