Question

In the given figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of $$\Delta$$ABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.

Answer 1

Given that $$X, Y$$ and $$Z$$ are the midpoints of the side $$AB, BC$$ and $$CA$$ respectively.
By midpoint theorem
$$XZ || BC$$ and $$XZ$$ $$=\dfrac{1}{2}$$ $$BC$$
$$BC = 11 cm$$
$$\Rightarrow XZ = \dfrac{BC}{2} = \dfrac{11}{2} = 5.5 cm$$
Similarly,

$$XY || AC$$ and $$XY$$ $$=\dfrac{1}{2}$$ $$AC$$
$$AC = 9 cm$$

$$XY = \dfrac{AC}{2} = \dfrac{9}{2} = 4.5$$ cm

$$YZ || AB$$ and $$YZ$$ $$=\dfrac{1}{2}$$ $$AB$$
$$AB = 5 cm$$
$$YZ = \dfrac{AB}{2} =\dfrac{5}{2} = 2.5$$ cm