In the given figure, PQRS is a parallelogram with \(PS=7\) cm, \(PT=4\) cm and \(PV=5\) cm. What is the length of \(RS\) in cm? (The diagram is representative.)
Show Hint
- For any parallelogram, the product \(\text{base} \times \text{height}\) is invariant.
- Perpendicular distances from the same vertex to opposite sides can be used as heights with the corresponding bases.
Step 1: In a parallelogram, the area is \( \text{base} \times \text{corresponding height} \).
Using base \(PS\) and its perpendicular height \(PT\):
\[
\text{Area}= PS \times PT = 7 \times 4 = 28 \ \text{cm}^2.
\]
The same area can be written using base \(RS\) and the perpendicular distance from \(P\) to \(RS\), which is \(PV\):
\[
\text{Area}= RS \times PV = RS \times 5.
\]
Equating the areas,
\[
RS \times 5 = 28 \quad \Rightarrow \quad RS=\frac{28}{5}\ \text{cm}.
\]
