Question

In ΔXYZ, M and N are mid-points of XY and XZ respectively. P and Q are mid-points of XM and XN. If PQ = 2.8 cm, find the length of YZ.

Answer 1

Step 1:

P and Q are mid-points of XM and XN.

According to the Midpoint Theorem, PQ = `1/2` MN

So, MN = 2 × PQ

MN = 2 × 2.8 cm = 5.6 cm

Step 2:

M and N are mid-points of XY and XZ

According to the Midpoint Theorem, MN = `1/2` YZ

So, YZ = 2 × MN

YZ = 2 × 5.6 cm = 11.2 cm

The length of YZ is 11.2 cm.