In ΔABC, P and Q are the middle points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR:RQ=1:4. If PR=5 cm, then BC= ?

By the Midpoint Theorem in ΔABC, since P and Q are midpoints of AB and AC:
PQ=
2
1
​
BC⟹BC=2⋅PQ
We are given the ratio PR:RQ=1:4, and PR=5 cm.

Therefore, RQ=4×PR=4×5=20 cm.

The total length of segment PQ is:

PQ=PR+RQ=5+20=25 cm
Now, calculating BC:

BC=2×25=50 cm