Question

Use the side-splitter theorem to solve for x in the triangle below.

a) \(x = 12\)
b) \(x = 8\)
c) \(x = 6\)
d) \(x = 10\)

Answer 1

The side-splitter theorem can be used to solve for x in the given triangle. By setting up a proportion using the lengths of the intersected sides, we can find the value of x.

Step-by-step explanation:

The side-splitter theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally. In the given triangle, the side-splitter theorem can be used to solve for x. Let's assume that the line is parallel to side AC and intersects side AB and side BC at points D and E respectively. According to the side-splitter theorem, we can set up a proportion:

(AD/DB) = (CE/EB)

Using the values given in the diagram, we can substitute the given lengths for AD, DB, CE, and EB:

(x/8) = (3/(3 + x))

Cross-multiplying and solving for x:

x(3 + x) = 8 * 3

x^2 + 3x - 24 = 0

Factoring the quadratic equation:

(x + 8)(x - 3) = 0

Solving for x:

x = -8 or x = 3

Since x cannot be negative in this context, the value of x is 3.