Question 256013
Let side opposite 90 = x
Let side opposite 30 = (1/2)x
Let side opposite 60 = (sqrt(3)/2)x
Perimeter = 12, so
(i) {{{x + (1/2)x + (sqrt(3)/2)x = 12}}}
solving for x, we get
(ii) {{{(3/2)x + (sqrt(3)/2)x = 12}}}
multiply by 2 to get
(iii) {{{3x + x*sqrt(3) = 24}}}
factor out an x to get
(iv) {{{x(3+sqrt(3)) = 24}}}
dividing, we get
(v) {{{x = 24/(3+sqrt(3))}}}
So,
side opposite 90 = 24/(3+sqrt(3))
side opposite 30 = 12/(3+sqrt(3))
side opposite 60 = 12sqrt(3)/(3+sqrt(3))
using these 3 lengths, our perimeter =12.
we want a + b + c values. I think we have them. The area formula is a bit confusing.