E and F are points on the sides PQ and PR respectively of a $\triangle PQR$ and EF || QR. If PE = 2·5 cm, PQ = 6 cm and PF = 4·5 cm, find the lengths of RF and PR.

Step 1: Apply Basic Proportionality Theorem

Since EF is parallel to QR in $\triangle PQR$, we can apply the Basic Proportionality Theorem (also known as Thales's Theorem). This theorem states that if a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Step 2: Calculate EQ

We are given the total length of side PQ and the length of segment PE. To find the length of EQ, we subtract PE from PQ.

Step 3: Substitute values and solve for FR

Now we substitute the known values into the proportionality equation. We have PE = 2.5 cm, EQ = 3.5 cm, and PF = 4.5 cm. We can then solve for FR.

Step 4: Calculate PR

Finally, to find the total length of side PR, we add the lengths of its segments PF and FR.

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