Question

In 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 AC = 9 cm
X and Y are the midpoints of side AB and BC.
The segment joining midpoints of any two sides of a triangle is parallel to the third side and half of it.
$XY=\frac{1}{2}AC$
$XY=\frac{1}{2}\times 9=4.5\text{cm}$
Given AB = 5 cm
Z and Y are the midpoints of side AC and BC.
The segment joining midpoints of any two sides of a triangle is parallel to the third side and half of it.
$YZ=\frac{1}{2}AB$
$YZ=\frac{1}{2}\times 5=2.5\text{cm}$
Given BC = 11 cm
Z and X are the midpoints of side AC and AB.
The segment joining midpoints of any two sides of a triangle is parallel to the third side and half of it.
$XZ=\frac{1}{2}BC$
$XZ=\frac{1}{2}\times 11=5.5\text{cm}$
Hence the measures of XY, YZ and XZ are 4.5 cm, 2.5 cm and 5.5 cm.