Question 1070786
{{{x^2+(x+7)^2=(x+x+7-4)^2}}}
{{{x^2+(x^2+14x+49)=(2x+3)^2}}}
{{{2x^2+14x+49=4x^2+12x+9}}}
{{{2x^2-2x-40=0}}}
{{{x^2-x-20=0}}}
{{{(x-5)(x+4)=0}}}
Two solutions but only one is positive,
{{{x-5=0}}}
{{{x=5}}}
The shortest side is {{{x}}}{{{cm}}} long, so the shortest side is 5 cm.