Question

In the given figure, PQRS is a parallelogram with $PS = 7~\text{cm}$, $PT = 4~\text{cm}$ and $PV = 5~\text{cm}$. What is the length of $RS$ in cm? (The diagram is representative.)

• A. $\dfrac{20}{7}$
• B. $\dfrac{28}{5}$
• C. $\dfrac{9}{2}$
• D. $\dfrac{35}{4}$

Hint:

For a parallelogram with right angles, use Pythagoras' theorem to find missing side lengths.

Answer 1

The Correct Option is B

Since $PQRS$ is a parallelogram, we know that opposite sides are equal in length. Thus, $RS=PQ=7~\text{cm}$. However, we can use the Pythagorean theorem to calculate the length of $RS$.
Using the right triangle $PVT$, we know: \[ \text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2 = 4^2 + 5^2 = 16 + 25 = 41 ⇒ RS = \sqrt{41} \approx 6.4~\text{cm}. \]