Question 388987
{{{a + 2a + 3a = 180}}}
{{{6a = 180}}}
{{{a = 30}}}
{{{2a = 60}}}
{{{3a = 90}}}
The shortest side is opposite the smallest angle
the ratios of the sides of a 30-60-90 triangle are
{{{1}}}:{{{sqrt(3)}}}:{{{2}}}
{{{1/sqrt(3) = 5*sqrt(3)/x}}}
{{{x = 5*sqrt(3)*sqrt(3)}}}
{{{x = 15}}}
The next longer side is 15 units long
check:
sides are:
opposite 30:{{{5*sqrt(3)}}}
opposite 60:{{{15}}}
opposite 90:{{{10*sqrt(3)}}}
{{{(5*sqrt(3))^2 + 15^2 = (10*sqrt(3))^2}}}
{{{75 + 225 = 300}}}
{{{300 = 300}}}
OK