Question

A warehouse had a square floor with area 10000 sq. meters. A rectangular addition was built along one entire side of the warehouse that increased the floor by one-half as much as the original floor. How many meters did the addition extend beyond the original building?

Answer 1

Hint: Assume that the length of the original side of the square floor is x meters. Now, calculate the area using the formula, \[Area=\left( side \right)\left( side \right)\] . It is given that the area of the square floor is equal to 10,000 sq. meters. Now, calculate the value of x. After a rectangular addition, one entire side of the square floor is increased by one half of the original side of the square floor.

Complete step by step answer:
According to the question, we have been given that a warehouse had a square floor with area 10000 sq. meters.
The area of the square floor = 10,000 sq. meters ………………………………………(1)
Let us assume that the length of the original side of the square floor is x meters.
Now, the side of the square floor = x meters …………………………………………….(2)
We know the formula, \[Area=\left( side \right)\left( side \right)\] ………………………………………..(3)
Using equation (2) and equation (3), calculating,
The are of the square floor = \[\left( x \right)\left( x \right)={{x}^{2}}\] ……………………………………(4)
From equation (1), we also have the area of the square floor.
Now, on comparing equation (1) and equation (3), we get
\[\begin{align}
  & \Rightarrow {{x}^{2}}=10000 \\
 & \Rightarrow x=\sqrt{10000} \\
 & \Rightarrow x=100 \\
\end{align}\]
So, the original side of the square floor is 100 meters ……………………………………….(5)
It is also given that a rectangular addition was built along one entire side of the warehouse that increased the floor by one-half as much as the original floor.
From equation (5), we have calculated the original side length of the square floor.
The length of each side of the square after a rectangular addition = 100 meters + half of 100 meters = \[\left( 100+\dfrac{1}{2}\,of\,100 \right)\] meters = 100 meters + 50 meters = 150 meters ………………………………….(6)
We have to find the length that is added to the side of the square floor.
From equation (5) and equation (6), we have the original side of the square floor and the length of each side of the square after a rectangular addition respectively.
The length in increase = \[\left( 150-100 \right)\] meters = 50 meters.

Hence, the addition extends beyond the original building is 50 meters.

Note: In this question, one might think that after a rectangular addition to the square floor, the area becomes half more than that of the original area of the floor. This is wrong because it is given that after a rectangular addition, the length of the square floor increases by one half of the entire side of the original square floor.