Question 334341
{{{S^2+S^2=(S+10)^2}}}
{{{2S^2=S^2+20S+100}}}
{{{S^2-20S-100=0}}}
Complete the square,
{{{(S^2-20S+100)-100=100}}}
{{{(S-10)^2=200}}}
{{{S-10=0 +- sqrt(200)}}}
{{{S=10 +- 5sqrt(8)}}}
Only the positive result makes sense here.
{{{highlight(S=10 + 5sqrt(8))}}}cm
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{{{H=10+S}}}
{{{highlight(H=20+5sqrt(8))}}}cm