Question

The length of a rectangular hall is 16 meters, if it can be partitioned into two equal square rooms what is the length of the partition.
(a). 16m
(b). 8m
(c). 14m
(d). 32m

Answer 1

Hint: We will use the formula of the area of the rectangle and the area of the square to find what is required in the question. Area of the rectangle is given as A = lb, where l is the length of the rectangle and b is the breadth of the rectangle and the area of square is given as side square.

Complete step-by-step answer:

Given a rectangular hall of length of 16 meters, the hall is then partitioned into two equal square rooms, we have to find out the length of the partition.
The figure of the given situation can be illustrated as.

To find out the length of the partition of the square room, we will assume the breadth of the rectangular hall as b and the length of the partitioned hall as a.
We know that the area of the rectangle is given by A = lb, where l is the length of the rectangle and b is the breadth of the rectangle.
Given that the length of the rectangular hall is 16m. then substituting this value in the formula of area of rectangle we have,
Area of the rectangular hall = 16b = 16b $m^2$
Now because the hall is partitioned into two equal square rooms therefore, area of each new room will be half of the area of the rectangular hall, that is,
Area of each new room = \[\dfrac{16b}{2}=8b {{m}^{2}}\] ….(i)
Now we have the formula of area of square as side square.
Since, we have taken the length of the new room as a, then the area of the room becomes a2….(ii)
Equating equation(i) and equation (ii) we have,
 \[{{a}^{2}}=8b\]
Substituting the value of b = 2,
\[\Rightarrow {{a}^{2}}=(8)(2)=16m\]
\[\Rightarrow a=\sqrt{16}=4m\]
This is not in the option.
Substituting b = 8,
\[\Rightarrow {{a}^{2}}=(8)(4)=64m\]
\[\Rightarrow a=\sqrt{64}=8m\]
Therefore, the length of the partitioned hall will be 8m, which is option (b).

Note: The possibility of error in this question can assume the new length as half of the previous length that is the new length becomes 8m directly, which can be the correct answer but the solution process is wrong because the shape of the room changes from rectangle to square.