E and F are points on the sides PQ and PR respectively of a △PQR and EF || QR. If PE = 2·5 cm, PQ = 6 cm and PF = 4·5 cm, find the lengths of RF and PR.
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Step-by-Step Solution
Step 1: Apply Basic Proportionality Theorem
Since EF is parallel to QR in △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.