Question 366930
Since it's a right triangle, it obeys the Pythagorean theorem,
{{{a^2+b^2=h^2}}}
{{{(h-9)^2+(h-2)^2=h^2}}}
{{{h^2-18h+81+h^2-4h+4=h^2}}}
{{{h^2-22h+85=0}}}
{{{(h-7)(h-15)=0}}}
Two solutions:
{{{h=7}}}
Then {{{a=7-9}}}
This is not a possible solution since it leads to a negative length.
.
.
.
{{{h-15=0}}}
{{{highlight(h=15)}}}cm
.
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{{{a=15-9}}}
{{{highlight(a=6)}}}cm
.
.
{{{b=15-2}}}
{{{highlight(b=13)}}}cm