Question

IV. Find x using quadratic formula.

Answer 1

The value of x of the similar triangles are: x = 9.735 or -0.0685

How to find the length of similar triangles?

Two triangles are said to be similar if the ratio of their corresponding sides are congruent and as such:

(x - 1)/2x = (15 - x)/(x + 2)

Cross multiply to get:

(x - 1)(x + 2) = 2x(15 - x)

x² + x - 2 = 30x - 2x²

3x² - 29x - 2 = 0

Using quadratic formula of:

x =
`\frac{-b \pm \sqrt{b^(2) - 4ac } }{2a}`

Thus:

x =
`\frac{-(-29) \pm \sqrt{(-29)^(2) - 4(3 * -2) } }{2(3)}`

x = (29 ± √865)/6

x = 9.735 or -0.0685