Question

What is the vale of x?

Answer 1

Since the triangles are similar, the following is true:

  20        x+6
------- = -------
2x -6       36

Then (20)(36) = (x+6)(2)(x-3) = 2[x^2+3x-18], or

720 = 2[x^2+3x-18], or 360 = x^2 + 3x - 18.

Then x^2 + 3x - 18 - 360 = 0.  This is a quadratic equation which can be solved using the quadratic formula, among other approaches.  Please apply the quadratic formula here, using a=1, b=3 and c= -378, to find x.

Answer 2

Since they are similar
36/x+6=2x-6/20