The length of the rectangular dining hall is twice its breadth. Let \[x\] represent the breadth of the hall. What is the area of the floor of the hall in terms of \[x\]?

Hint: We will first consider the given information that is the length of the rectangular dining hall is twice its breadth. We are given that the breadth of the hall is represented by \[x\]. As given in the question we will find the length of the hall which is given by \[2x\]. Now, to determine the area of the floor of the hall, we will use the area of the rectangle formula, \[A = lb\], and substitute the values in it. Thus, we will get the desired result.

Complete step by step answer:

We will first consider the given data that is the breadth is represented by \[x\].
Now, as we are given in the question that the length of the rectangular hall is twice its breadth.
So, we will get the length of the dining hall as \[2x\] using the given condition.

Now, we have to evaluate the area of the floor of the hall in terms of \[x\].
So, we will use the area of the rectangle to determine the area of the floor.
The area of the rectangle is given by \[A = lb\].
Thus, we will substitute the values of length and breadth in the formula and we get,
\[
   \Rightarrow A = x\left( {2x} \right) \\
   \Rightarrow A = 2{x^2} \\
 \]
Hence, we can conclude that the area of the floor of the hall in terms of \[x\] is \[2{x^2}\].

Note: Remember the area of rectangle that is \[A = lb\]. As we are given that the breadth of the rectangle to be \[x\] so, we can easily determine the length of the rectangle using the given information. As we need to find the area of the floor of the hall so, we have used the area of rectangle only as the room is rectangular in shape which implies that the shape of the floor is also rectangular. Do the substitution of the values in the formula properly and avoid doing calculation mistakes.