Question

segment \\(\overline{bd}\\) bisects \\(\angle abc\\). solve for \\(x\\). round to the nearest tenth, if necessary. (image not necessarily to scale.)

image of triangle abc with d on ac, cd=5, da=6, bc=10, ba=x

answer attempt 1 out of 2
\\(x = \square\\) submit answer

Explanation:

Step1: Apply Angle - Bisector Theorem

The Angle - Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides. So, \(\frac{CD}{DA}=\frac{BC}{BA}\).
Given \(CD = 5\), \(DA=6\), \(BC = 10\), and \(BA=x\). Substitute the values into the formula: \(\frac{5}{6}=\frac{10}{x}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(5x=6\times10\).
Simplify the right - hand side: \(5x = 60\).
Divide both sides by \(5\): \(x=\frac{60}{5}\).

Answer:

\(x = 12\)