The problem appears to be in Bengali and seems to involve a triangle $\triangle PQR$, with given information:

• $\angle PRQ = 60^\circ$,
• $PQ = 1$ (possibly a unit length),
• $PR = 8 \, \text{cm}$.

The task is to calculate the length of $QR$.

To solve this, let’s assume the triangle forms a relationship that allows using trigonometry or the cosine rule since one angle and two sides are given.

Solution:

Using the cosine rule: $QR^2 = PR^2 + PQ^2 - 2 \cdot PR \cdot PQ \cdot \cos(\angle PRQ)$

Substituting the given values:

• $PR = 8$,
• $PQ = 1$,
• $\cos(60^\circ) = \frac{1}{2}$,

$QR^2 = 8^2 + 1^2 - 2 \cdot 8 \cdot 1 \cdot \frac{1}{2}$ $QR^2 = 64 + 1 - 8$ $QR^2 = 57$ $QR = \sqrt{57}$

Thus, $QR = \sqrt{57} \approx 7.55$, but since the problem specifies options involving square roots, $QR$ could be left as $\sqrt{57}$.

Answer:

Among the options provided, the length $QR$ aligns with the calculation.

If you would like me to refine this further or explain in detail, let me know!

Here are 5 related questions for further understanding:

1. How does the cosine rule apply to non-right triangles?
2. What is the importance of knowing one angle when solving triangles?
3. How can trigonometric identities simplify such problems?
4. What alternative methods exist for solving this if no angle is given?
5. How does understanding triangle properties help in real-world geometry problems?

Tip: Always double-check the unit of measurement and ensure consistency in trigonometric problems.