Question

The area of a rectangular banquet hall is 7,400 squre feet. The length of one side of the hall is 82 feet. Explain how you can use compatible numbers to estimate the width of the hall.

Answer 1

90.2 ft.

Explanation:

We can divided both numbers to find the answer, and that can be done rapidly:
`(7400)/(82) = 90.2`

However, 7400 and 82 are too different number to use them as compatible numbers, but we can simplify the fraction step by step, we can divide each part by 2, which would give
`(3700)/(41)`, and we will have minor numbers, making easier the division.

In addition, this division is allowed because it's based on the definition of a rectangle area, which is:
`A_(rectangle) = (height)(width)`

The problem gives us the total are and one side, we just need to replace values and isolate the side missing:

`(A_(rectangle) )/(height) =(width)\\(width) = (7400)/(82) = 90.2`

Therefore, the width of the hall is 90.2 ft.

Answer 2

Answer: Width of rectangle = 90 approximately.

Explanation:

Since we have given that

Area of a rectangular banquet hall = 7400 square feet

Length of rectangular banquet hall = 82 feet

Since we know the formula for area of rectangle i.e.

`Area of rectangle=Length* Breadth\\\\7400=82* Breadth\\\\(7400)/(82)=Breadth\\\\90.24\ feet=Breadth`

If we round it to hundredths after decimal then, it becomes

Width of rectangle= 90.2 feet

If we want it to be whole number then it will be considered it as

Width of rectangle= 90 feet approximately.