Question

A floor is $ 5\;m $ long and $ 4\;m $ wide. A square carpet of sides $ 3\;m $ is laid on the floor. Find the area of the floor that is not carpeted.

Answer 1

Hint: Find the area of the floor and then find the area of each square carpet and find the maximum area that can be covered with the help of the carpets on the floor. Do not just considere one square carpet till the difference between the areas will be less than the area of square carpet.

Complete step-by-step answer:
The floor is $ 5\;m $ long and $ 4\;m $ wide. A square carpet of sides $ 3\;m $ is laid on the floor.
As per given in the statement, a floor is $ 5\;m $ long and $ 4\;m $ wide. So, the area of the rectangular shape is always the product of the length to the breadth.
So, the area of the floor is equal to
 $ 5\;m \times 4\;m = 20\;{m^2} $ .
The carpet is in the form of the square with side as $ 3\;m $ . The area of the square shape is always side square.
So, the area of each carpet is equal to
 $ {\left( {3\;m} \right)^2} = 9\;{m^2} $ .
As the area of each carpet is equal to $ 9\;{m^2} $ and the area of the floor is equal to $ 20\;{m^2} $ . So, the maximum number of carpets that can be used to cover the floor is equal to $ 2 $ .
The area covered by the carpets is equal to
 $ 9 \times 2 = 18\;{m^2} $ .
So, the area that is not carpeted is equal to
 $ 20\;{m^2} - 18\;{m^2} = 2\;{m^2} $ .
So, the area of the floor that is not carpeted is equal to $ 2\;{m^2} $ .
So, the correct answer is “ $ 2\;{m^2} $ ”.

Note: Avoid calculation mistakes in this question to avoid the confusion and also take care of the shapes of the floor and carpet and also the formulas for the area of each type of figure. Wrong application of formula wil lead to incorrect results.