Question 169382
Okay, let us illustrate the triangle:
{{{drawing(400,400,-1,18,-1,12,graph(400,400,-1,18,-1,12),blue(triangle(1,1,16,1,1,9)),red(line(1,2,2,2)),red(line(2,2,2,1)),locate(8.5,6,37in),locate(8,.85,a),locate(.50,5,b))}}}
We know the {{{Ratio=width/height=a/b=16/9}}}
By Ratio we get, {{{a=(16/9)b}}} ------------------> eqn 1
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Consider the Sides of the Triangle, By Pyth.Theorem:
{{{c^2=a^2+b^2}}} -------> eqn 2
Subst. eqn 1 in eqn 2:
{{{37^2=((16/9)(b))^2+b^2}}}
{{{1369=(256/81)b^2+b^2}}}
{{{1369=3.1605b^2+b^2=4.1605b^2}}}
{{{cross(1369)329.047/cross(4.1605)=cross(4.1605)b^2/cross(4.1605)}}}
{{{b=sqrt(329.047)}}}
{{{highlight(b=18.14inches)}}}, Height
Go back eqn 1:
{{{a=(16/9)(18.14)=highlight(32.25inches=a)}}}, Width
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Checking by the {{{Ratio=16/9}}}
{{{a/b=32.25/18.14=1.7778}}} ------> {{{16/9=1.7777778}}}; Close enough I guess 
Rewriting the Traingle:
{{{drawing(400,400,-1,18,-1,12,blue(triangle(1,1,16,1,1,9)),red(line(1,2,2,2)),red(line(2,2,2,1)),locate(8.5,6,37in),locate(7.5,.85,a),locate(.50,5,b),locate(0,4.5,red(18.14in)),locate(8.2,.85,red(32.25in)))}}}
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thank you,
Jojo