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

If BC = 6.5, CD = 7.8, and AD = 12.2, find AB to the nearest tenth.-example-1
User Vladiim
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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.
User Gdrt
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