Question 882967
Let {{{ x }}} = the length of
one of the opposing sides
{{{ 160 - 2x }}} = the length
of the 3rd side
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{{{ A = x*( 160 - 2x ) }}}
{{{ A = -2x^2 + 160x }}}
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When the form of the equation is
{{{ f(x) = a*x^2 + b*x + c }}}
The max is at {{{ x = -b/(2a) }}}
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{{{ x[max] = -160 / (2*(-2)) }}}
{{{ x[max] = 40 }}}
and
{{{ 160 - 2x = 160 - 80 }}}
{{{ 160 - 2x = 80 }}}
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The 3 sides are 40, 40, and 80
Here's the plot:
{{{ graph( 400, 400, -10, 100, -500, 5000, -2x^2 + 160x ) }}}