Question 1058527
Formula for perimeter of rectangle:
{{{ P = 2W + 2L }}}
{{{ P = 688 }}} ft
{{{ 688 = 2W + 2L }}}
{{{ 344 = W + L }}}
{{{ L = 344 - W }}}
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Formula for area of a rectangle:
{{{ A = W*L }}}
{{{ A = W*( 344 - W ) }}}
{{{ A = -W^2 + 344W }}}
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The formula for {{{ W[max] }}} is
{{{ W[max] = -b/(2a) }}}
{{{ a = -1 }}}
{{{ b = 344 }}}
{{{ W[max] = -344/(2*(-1) ) }}}
{{{ W[max] = 172 }}}
{{{ L[max] = 344 - W }}}
{{{ L[max] = 172 }}}
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Plug this result back into equation
{{{ A[max] = -172^2 + 344*172 }}}
{{{ A[max] = -29584 + 59168 }}}
{{{ A[max] = 29584 }}}
{{{ A[max] = 172^2
also
{{{ A[max] = W*L }}}
{{{ A[max] = 172*172 }}}
This shows that the maximum area is a square
( which is always true )
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Here's the plot od {{{ A = -W^2 + 344W }}}
{{{ graph( 400, 400, -100, 500, -3500, 35000, -x^2 + 344x ) }}}