Question 1154296
 A rancher plans to use {{{340}}} yards of fencing for a corral and divide it into two parts with the fence parallel to the shorter sides of the corral. 

=> it is a rectangle divided into two parts; so, if {{{L}}} is the longer side and {{{W}}} is the shorter side, you will have {{{2L}}} and {{{W}}} whose sum is {{{340}}}


find the dimensions of the corral if its area is to be {{{4700}}} square yards. 


perimeter in this case would be:


{{{2L + 3W = 340}}}....solve for {{{L}}}

{{{2L = 340 - 3W}}}

{{{L = 340/2 - (3/2)W}}}

{{{L = 170 - 1.5W}}}.........eq.1


The area:


{{{A=L*W}}}......plug in desired area and substitute {{{L}}} from eq.1

{{{4700=(170-1.5W)*W}}}.....solve for {{{W}}}

{{{4700=170W-1.5W^2}}}

{{{1.5W^2-170W+4700=0}}}......use quadratic formula

{{{W=(-(-170)+-sqrt((-170)^2-4*1.5*4700))/(2*1.5)}}}

{{{W=(170+-sqrt(28900-28200))/3}}}

{{{W=(170+-sqrt(700))/3}}}

{{{W=(170+-10sqrt(7))/3}}}


exact solutions:

{{{W=(170+10sqrt(7))/3}}} or
{{{W=(170-10sqrt(7))/3}}}

approximate solutions:

{{{W=65.49}}} or
{{{W=47.85}}}


find {{{L}}}

{{{L = 170 - 1.5(170+10sqrt(7))/3}}}.........eq.1

{{{L = 170 - (170+10sqrt(7))/2}}} or
{{{L = 170 - (170-10sqrt(7))/2}}}


approximate solutions:

{{{L = 71.77}}} or
{{{L = 98.23}}}

so, you have:

{{{L = highlight(98.23)}}} and {{{W=highlight(47.85)}}}
{{{L = highlight(71.77)}}} and {{{W=highlight(65.49)}}}


check the perimeter:

{{{2L + 3W = 340}}}
{{{2*98.23 + 3*47.85 = 340}}}
{{{340.01= 340}}} round it
{{{340= 340}}}

or

{{{2L + 3W = 340}}}
{{{2*71.77 + 3*65.49 = 340}}}
{{{340.01= 340}}} round it
{{{340= 340}}}

check the area:

{{{4700=98.23*47.85}}}
{{{4700=4700.3055}}}round it
{{{4700=4700}}}

{{{4700=71.77*65.49}}}
{{{4700=4700.2173}}}round it
{{{4700=4700}}}