A rectangular plot has length 8 m greater than its breadth. If its area is 308 m², find the length of the plot.

Introduction / Context:
Relate dimensions of a rectangle using algebra: let breadth be b (in meters). Given that length is b + 8 and the area is 308, form a quadratic in b and solve. Then compute the length from b + 8.

Given Data / Assumptions:

• Length L = b + 8
• Area A = 308 m^2
• Area formula: A = L * b

Concept / Approach:
Set up b(b + 8) = 308 to obtain a quadratic. Solve for b, discard the negative root as a physical dimension, and add 8 to get L.

Step-by-Step Solution:
b(b + 8) = 308 ⇒ b^2 + 8b − 308 = 0Discriminant: 8^2 + 4*308 = 64 + 1232 = 1296 ⇒ √1296 = 36b = (−8 ± 36)/2 ⇒ b = 14 or b = −22 (reject)Length L = b + 8 = 14 + 8 = 22 m

Verification / Alternative check:
Area check: 22 * 14 = 308 m^2, matches the given area.

Why Other Options Are Wrong:
18 m and 20 m do not produce area 308 with an 8 m difference; “None of these” is unnecessary since 22 m fits perfectly; 24 m would imply breadth 16 m and area 384 m^2.

Common Pitfalls:
Arithmetic mistakes with the discriminant or selecting the negative breadth. Ensure units in m^2 for area.

Final Answer:
22 m