Question

Arbaz plans to tile his kitchen with square tiles. Each side of the tile is 10 cm. His kitchen is 220 cm in length and 180 cm in breadth. How many tiles will he need?

Answer 1

Hint: In this question, we first need to look into the basic definitions of algebra. Then assume that the number of tiles required as some variable and then equate the area of room with the area of the tiles that will be used.

Complete step-by-step answer:
Let us look at some of the basic definitions.
LINEAR EQUATIONS:
Equation: A statement of equality of two algebraic expressions involving two or more unknown variables is called equation.
Linear Equation: An equation involving the variables in maximum of order 1 is called a linear equation. Graph of a linear equation is a straight line.
Linear equation in one variable is of the form \[ax+b=0\].
Linear equation in two variables is of the form \[ax+by+c=0\]
Solution of an Equation- A particular set of values of the variables, which when substituted for the variables in the equation makes the two sides of the equation equal, is called the solution of the equation.
In geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as equiangular quadrilateral. The diagonals of a rectangle are equal.
Area of a rectangle with length l and breadth b is given by:
\[l\times b\]
In geometry, a square is a regular quadrilateral, which means it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length.
Area of a square with side length is given by:
\[s\times s={{s}^{2}}\]
Now, let us assume that the number of tiles required as x, area of the kitchen as A and area occupied by the total number of tiles used as B.
Given,
\[l=220,b=180,s=10\]
\[\begin{align}
 & \Rightarrow A=l\times b \\
 & \Rightarrow A=220\times 180 \\
 & \therefore A=39600c{{m}^{2}} \\
\end{align}\]
\[\begin{align}
 & \Rightarrow B=x\times {{s}^{2}} \\
 & \Rightarrow B=x\times {{\left( 10 \right)}^{2}} \\
 & \therefore B=x\times 100c{{m}^{2}} \\
\end{align}\]
As we already know that A = B we get,
\[\begin{align}
 & \Rightarrow 39600=x\times 100 \\
 & \Rightarrow x=\dfrac{39600}{100} \\
 & \therefore x=396 \\
\end{align}\]
Hence, he needs 396 tiles to tile his kitchen.

Note: Instead of assuming the number of tiles to be some variable we can directly calculate them by using the cross multiplication method. We consider that kitchen has an area of 39600 cm² then on dividing it with the area of the tiles we get the number of tiles required.
While calculating the areas we need to be careful while substituting the respective values in them. It is important that the number tiles assumed should be multiplied with the area of the tiles and then equate to the area of the kitchen. If done in the other way the result changes completely.