JAMB 2015 · UTME · Q19

Sine & cosine rules

In $\triangle XYZ$ , $XY = 3\text{ cm}$ , $XZ = 5\text{ cm}$ and $YZ = 7\text{ cm}$ . If the bisector of $\angle XYZ$ meets $XZ$ at $W$ , what is the length of $XW$ ?

Worked solution (try it first)

The bisector of an angle of a triangle cuts the opposite side in the ratio of the two sides next to that angle.
So $XW : WZ = YX : YZ = 3 : 7$ .
$XZ = 5$ cm is split into $3 + 7 = 10$ parts, so $XW = \frac{3}{10} \times 5$ .
So $XW = 1.5$ cm, option A.

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