B is between A and C. If AB=x squared, BC=9x and AC=36, find the value(s) of x, AB, and BC.
Consider a line segment with endpoints A and C with B a point on segement AC. The measure of AB = x^2, the measure of BC = 9x, and the measure of AC = 36. Then AB + BC = AC
x^2 + 9x = 36
x^2 + 9x -36 = 0
(x + 12)(x - 3) = 0
x + 12 = 0 or x - 3 = 0
x = -12 x = 3
Don't use x = -12 because a measure of a line segment cannot be negative. Therefore x = 3
AB = x^2
AB = 3^2
AB = 9
BC = 9x
BC = 9(3)
BC = 27