Question

If BC = 6.5, CD = 7.8, and AD = 12.2, find AB to the nearest tenth.

Answer 1

This can be solved using the angle bisector theorem. Note that line segment AD is the angle bisector of triangle DAB from angle DAB. Therefore, we know that the ratios $\frac{\text{AD}}{\text{CD}}$ and $\frac{\text{AB}}{\text{CB}}$ are equal. Solving, we get $\frac{\text{12.2}}{\text{7.8}}=\frac{\text{AB}}{\text{6.5}}$. Cross multiplying, we get $79.3 = 7.8x$, and solving this equation we get $x = 10.1666... \approx 10.2$. 10.2 is your answer.