Question 1146067
Let the length of the middle side = {{{ x }}} in.
The length of the shortest side = {{{ x - 7 }}} in.
The length of the hypotenuse = {{{ x + 1 }}} in.
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{{{ x^2 + ( x-7 )^2 = ( x + 1 )^2 }}}
{{{ x^2 + x^2 - 14x + 49 = x^2 + 2x + 1 }}}
{{{ x^2 - 16x + 48 = 0 }}}
{{{ ( x - 4 )*( x - 12 ) = 0 }}} ( by looking at it )
{{{ x = 4 }}}
{{{ x = 12 }}}
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I'll choose {{{ x = 4 }}}
{{{ x^2 + ( x-7 )^2 = ( x + 1 )^2 }}}
{{{ 4^2 + ( 4-7 )^2 = ( 4 + 1 )^2 }}}
{{{ 16 + 9 = 25 }}}
This doesn't work because you can't take 7 in from 4 in
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{{{ x = 12 }}}
{{{ x^2 + ( x-7 )^2 = ( x + 1 )^2 }}}
{{{ 12^2 + ( 12-7 )^2 = ( 12 + 1 )^2 }}}
{{{ 144 + 25 = 169 }}}
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5 - 12 - 13 are the sides