Question

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.) 

• A. \( \frac{20}{7} \)
• B. \( \frac{28}{5} \)
• C. \( \frac{9}{2} \)
• D. \( \frac{35}{4} \)

Hint:

- In a parallelogram, opposite sides are equal.
- Use the Pythagorean theorem to calculate the length of the diagonal or side in a right triangle.

Answer 1

The Correct Option is A

We are given a parallelogram PQRS where the sides PS, PT, and PV are given as 7 cm, 4 cm, and 5 cm respectively. We are tasked with finding the length of the side RS. In a parallelogram, opposite sides are equal. So, \( RS = PQ \). Using the properties of the triangle \( PTV \) and the Pythagorean theorem, we can find the length of RS: \[ RS = \sqrt{(PS)^2 + (PV)^2} = \sqrt{7^2 + 5^2} = \sqrt{49 + 25} = \sqrt{74} = \frac{20}{7} \] Thus, the length of RS is \( \frac{20}{7} \) cm.