A rectangular room has length 4 meters. It can be partitioned into two equal square rooms (by building a wall along the breadth). What is the side length (and hence the partition length) of each resulting square room, in meters?

Introduction / Context:If a rectangle can be exactly divided into two equal square rooms by a partition parallel to the breadth, then the rectangle’s length must be twice its breadth; equivalently, the rectangle is composed of two congruent squares side by side.

Given Data / Assumptions:

• Rectangle length L = 4 m
• Two equal squares produced by one partition
• Let square side be s; then L = 2s (two squares along the length)

Concept / Approach:Write L = 2s and solve for s. The partition that separates the two squares has length equal to the side of the square (i.e., the original breadth), which is s.

Step-by-Step Solution:L = 2s ⇒ 4 = 2s ⇒ s = 2 mPartition length (the wall across the breadth) = s = 2 m

Verification / Alternative check:Each square would be 2 m × 2 m; placing two such squares along length makes a 4 m × 2 m rectangle, consistent with L = 4 m.

Why Other Options Are Wrong:1 m or 4 m would not form two equal squares with total length 4 m; “Data inadequate” is incorrect because L alone suffices.

Common Pitfalls:Assuming partition orientation incorrectly; the standard interpretation is a wall parallel to breadth, yielding two squares placed along the length.

Final Answer:2