Question

In the given figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of $∆$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 = $\frac{1}{2}$BC
BC = 11 cm
$\Rightarrow$XZ = $\frac{\mathrm{BC}}{2}=\frac{11}{2}=5.5\mathrm{cm}$
Similarly,
$$\begin{gathered} \mathrm{XY}=\frac{\mathrm{AC}}{2}=\frac{9}{2}=4.5\mathrm{cm} \\ \mathrm{YZ}=\frac{\mathrm{AB}}{2}=\frac{5}{2}=2.5\mathrm{cm} \end{gathered}$$