The length of a rectangular hall is 5 m more than its breadth. If the area of the hall is 750 square metres (m^2), find the length of the hall in metres.

Introduction / Context:
This is a standard rectangle word problem that tests forming and solving a quadratic equation. If you know that length is a fixed amount more than breadth and you also know the area, you can express both dimensions in terms of one variable and solve for the missing dimension.

Given Data / Assumptions:

• Area = 750 m^2
• Length = breadth + 5 m
• Let breadth = b m
• Then length = (b + 5) m

Concept / Approach:
Area of a rectangle = length * breadth. Substitute the expression for length and solve the resulting quadratic: b(b+5) = 750. Then compute the length.

Step-by-Step Solution:
Area = b*(b + 5) = 750 b^2 + 5b - 750 = 0 Find two numbers with product -750 and sum 5: 30 and -25 (b + 30)(b - 25) = 0 So b = 25 (reject b = -30 because length cannot be negative) Length = b + 5 = 25 + 5 = 30 m

Verification / Alternative check:
If breadth is 25 m and length is 30 m, area = 25*30 = 750 m^2, which exactly matches the given area.

Why Other Options Are Wrong:
20 m: would imply breadth 15 m, area 300 m^2, not 750 m^2. 25 m: would imply breadth 20 m, area 500 m^2. 35 m: would imply breadth 30 m, area 1050 m^2. 40 m: would imply breadth 35 m, area 1400 m^2.

Common Pitfalls:
Using length - 5 instead of length = breadth + 5. Choosing the negative root for breadth. Forgetting that area uses square units (m^2) while dimensions are in metres (m).

Final Answer:
Length of the hall = 30 m