CPhill

(x/(2-x))^2=6/15   simplifying, we have

x^2 / ( x^2 - 4x + 4)  = 6 / 15      cross- multiply

15x^2  = 6(x^2 - 4x + 4)     divide both sides by 3

5x^2 = 2(x^2 - 4x + 4)

5x^2 = 2x^2 - 8x + 8

3x^2 + 8x - 8 = 0          divide both sides by 3

x^2 + (8/3)x - 8/3  = 0    complete the square

x^2 + (8/3)x + 16/9  = 8/3 + 16/9

(x + 4/3) ^2  = 24/9 + 16/9

(x + 4/3) ^2  = 40/9     take both roots

x + 4/3   = ±(2/3)√10

x = [ - 4 ± 2√10 ] / 3

We have this proportion....

 36 / 12 = x / 9    where x is the model door height

Cross-multiply

36*9 = 12 * x

324 = 12 *x    divide both sides by 12

27 = x      and that's the model height in centimeters

Z man winning and being right all the time.....oh....so it's a fantasy play....!!!!

Uh oh!!!!.......you're in trouble now, z man  !!!!

OK....how about (3 + 1/3)  ???

What is your play titled???......"The Odd Couple???"   (well....only one of them really is.....!!!)

Angle A = 37 degrees

The problem here is that we don't know if the "x" side lies across from A or B

If it lies across from A, then

x= 47.3  tan 37

If it lies across from B, then

x = 47.3  tan 53

If we had a 2ft x 1ft rectangle, we could put 8 of the tiles along one side and 4 along the other.....thus......8 x 4 = 32 tiles

81^x = 64   by taking the log of both sides, x = log64 / log 81

So

27^x+1 =  27^{( log64 / log 81  + 1)} = about 610.94