Question 1207295


Set up an equation for the perimeter using the total length of the fencing and the variables representing the width and length of the region.

{{{P=2(l+w)}}}

if a veterinarian wishes to use {{{156}}} feet of chain-link fencing , {{{P=156ft}}}


{{{156=2(l+w)}}}

{{{l+w=156/2}}}

{{{l+w=78}}}...solve for {{{l}}}

{{{l=78-w}}}......eq.1


if the total enclosed area is {{{864ft^2}}}, we have


{{{l*w=864}}}....substitute {{{l}}}

{{{(78-w)w=864}}}

{{{78w-w^2=864}}}

{{{0=w^2-78w+864}}}

using quadratic formula we get

{{{w = 3 (13 + sqrt(73))=64.63}}}=>larger width
{{{w = 3(13 - sqrt(73))=13.37}}} =>smaller width

calculate the lengths

{{{l=78-64.63=13.37}}}
{{{l=78-13.37=64.63}}}


answer:

{{{w=13.37ft}}} (smaller width) by {{{l=64.63ft}}}
{{{w=64.63ft}}} (lager width) by {{{l=13.37ft}}}