Question 732615
Use pythagorean theorem
{{{ x^2 + 7^2 = ( x + 1 )^2 }}}
{{{ x^2 + 7^2 = x^2 + 2x + 1 }}}
Subtract {{{ x^2 }}} from both sides
{{{ 49 = 2x + 1 }}}
{{{ 2x = 48 }}}
{{{ x = 24 }}}
{{{ x + 1 = 25 }}}
The perimeter is:
{{{ x + 7 + x + 1 = 24 + 7 + 25 }}}
{{{ 2x + 8 = 56 }}}
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check:
{{{ x^2 + 7^2 = ( x + 1 )^2 }}}
{{{ 24^2 + 7^2 = 25^2 }}}
{{{ 576 + 49 = 625 }}}
{{{ 625 = 625 }}}
OK