Question 750582
The area of a triangle is {{{ A = (1/2)*b*h }}}
Let {{{ h }}} = the height of the sail
Let {{{ b }}} = the foot of the sail
given:
{{{ A = 52 }}} ft2
{{{ h = b + 5 }}} ft
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{{{ A = (1/2)*b*h }}}
{{{ 52 = (1/2)*b*( b+5) }}}
{{{ 104 = b^2 + 5b }}}
{{{ b^2 + 5b - 104 = 0 }}}
I notice that {{{ 104 = 13*8 }}}, so I can guess that
{{{ b^2 + 5b - 104 = ( b + 13 )*( b - 8 ) }}}
{{{  ( b + 13 )*( b - 8 ) = 0 }}}
{{{ b = 8 }}} ( reject the negative answer )
and, since
{{{ h = b + 5 }}}
{{{ h = 13 }}}
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The height is 13 ft and the foot is 8 ft
check:
{{{ A = (1/2)*b*h }}}
{{{ A = (1/2)*8*13 }}}
{{{ A = 52 }}}
OK