Question 1087936
Let the ramp be {{{ r ||| inches long
Another leg is {{{ r - 1 }}} in long
The height of the ramp is {{{ r - 8 }}} in long
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Use pythagorean theorem
{{{ ( r - 1 )^2 + ( r - 8 )^2 = r^2 }}}
{{{ r^2 - 2r + 1 + r^2 - 16r + 64 = r^2 }}}
{{{ 2r^2 - 18r + 65 = r^2 }}}
{{{ r^2 - 18r + 65 = 0 }}}
complete the square:
{{{ r^2 - 18r + (18/2)^2 = -65 + (18/2)^2 }}}
{{{ r^2 - 18r + 81 = -65 + 81 }}}
{{{ ( r - 9 )^2 = 16 }}}
{{{ ( r - 9 )^2 = 4^2 }}}
{{{ r - 9 = 4 }}}
{{{ r = 13 }}}
and the other solution is:
{{{ r - 9 = -4 }}}
{{{ r = 5 }}}
( I can't use this solution because I cannot subtract {{{ 8 }}} from it )
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{{{ r = 13 }}}
{{{ r - 1 = 12 }}}
{{{ r - 8 = 5 }}}
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The height of the ramp is 5 in
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check answer:
{{{ ( r - 1 )^2 + ( r - 8 )^2 = r^2 }}}
{{{ 12^2 + 5^2 = 13^2 }}}
{{{ 144 + 25 = 169 }}}
{{{ 169 = 169 }}}
OK