Question

Each student in a classroom has a rectangular desk that measures 60cm by 45cm. Some of these desks are put together as shown in the diagram to form a large square table for a class activity.

Find:
(a)The least length of a side of the square.
(b)The number of rows and columns of desks need to form a square table.

Answer 1

Hint: Let us assume that x are the number of columns and y are the number of rows needed to make the square table. Now, multiplication of x with 60 cm is equal to multiplication of y with 45 cm. From this, we will get the relation between x and y. Now, to find the least side of the square by hit and trial method, put the minimum possible value of either x or y so that we will get x or y as integer because the number of rows and columns must be a positive integer.

Complete step by step answer:
The figure given in the above problem is as follows:

Now, let us assume that x is the number of columns and y is the number of rows which we needed to make a square table.
We know that all the sides of the square are equal so the length and breadth of the square is also equal. Using this concept we are going to multiply 60 cm by x and then equate this multiplication to the multiplication of y to 45 cm and we get,
$60x=45y$
Dividing 15 on both the sides of the above equation we get,
$\begin{align}
  & \dfrac{60x}{15}=\dfrac{45x}{15} \\
 & \Rightarrow 4x=3y \\
\end{align}$
Dividing 4 on both the sides we get,
$\begin{align}
  & \Rightarrow \dfrac{4x}{4}=\dfrac{3y}{4} \\
 & \Rightarrow x=\dfrac{3y}{4} \\
\end{align}$
The least positive integral value of y which can be possible is 4 because then that make the x as integer and we get,
$\begin{align}
  & x=\dfrac{3\left( 4 \right)}{4} \\
 & \Rightarrow x=3 \\
\end{align}$
From the above, we got the value of $x=3\And y=4$.
So, the minimum number of rows is 4 and the minimum number of columns is 3 which is required to make a square table,
And the least side of the square is multiplying 3 by 60cm we get,
$\begin{align}
  & 3\times 60 \\
 & =180cm \\
\end{align}$
Hence, the answer of part (a) is 180cm and the answer of part (b) is the number of rows equal to 4 and the number of columns equal to 3.

Note: To solve the above problem, you must know what a square is and its basic properties. Also, the problem which you could be facing is finding the minimum value of x and y. As x and y are the number of columns and rows and those values must be a natural number.