A trapezoid has an area of 144 square meters and an altitude of 4 meters. Its two bases have a ratio of 4:5. What is the perimeter of the trapezoid?

##x + g(x) + 72##
##b/B = 4/5##
##A = (B + b)/2 cdot h##
##144 = (B + 4/5 B)/2 cdot 4##
##72 = B + 4/5 B = 9/5 B Rightarrow B = 5/9 cdot 72 = 40##
##b = 4/5 cdot 40 = 32##
##B – b = 8##
There are infinitely many ##x##’s , ##y##’s such that the area of triangle is ##1/2 cdot 8 cdot 4 = 16##
: ##2p = x + y + 8##
##16 = sqrt{p(p-x)(p-y)(p-8)} = f(x, y)##
We want trapezoid’s perimeter = ##x + y + 40 + 32##