Question 844747
If we say that the longest side measures {{{10x}}} cm,
the lengths of the sides, in cm are {{{7x}}} , {{{9x}}} and {{{10x}}} .
That makes the perimeter, in cm equal to
{{{7x+9x+10x=78}}}
Solving
{{{7x+9x+10x=78}}}
{{{26x=78}}}
{{{x=78/26}}}
{{{x=3}}}
Then {{{7x=7*3=21}}} ,
{{{9x=9*3=27}}} , and
{{{10x=10*3=30}}} .
So the lengths of the sides are
{{{highlight(21cm)}}} ,{{{highlight(27cm)}}} , and {{{highlight(30cm)}}} .