Question

A scale drawing of a game room is shown below: A rectangle is shown. The length of the rectangle is labeled 2 inches. The width of the rectangle is labeled 4.5 inches. The scale is 1 to 30. What is the area of the actual game room in square feet? Round your answer to the nearest whole number.

Answer 1

The area of the actual game room is 56 square feet.

Explanation:

Given:

The length of the rectangle is labeled 2 inches. The width of the rectangle is labeled 4.5 inches. The scale is 1 : 30.

Now, to find the actual area of the actual game room in square feet.

Let the actual length be
`x.`

And let the actual width be
`y.`

So, as the scale is 1 : 30.

And, the length labeled is 2 inches and the width labeled is 4.5 inches.

If, 1 is equivalent to 30.

Thus, 2 is equivalent to
`x.`

Now, to get the actual length by using cross multiplication method:

`(1)/(30) =(2)/(x)`

By cross multiplying we get:

`x=60\ inches.`

Therefore, the actual length is 60 inches.

Now, to get the actual width we again use cross multiplication method:

If, 1 is equivalent to 30.

So, 4.5 is equivalent to
`y.`

`(1)/(30) =(4.5)/(y)`

By cross multiplying we get:

`y=135\ inches.`

Hence, the actual width is 135 inches.

Now, to get the area of the actual game room in square feet:

We convert the length and width of actual room in feet by using conversion factor:

12 inches = 1 feet.

60 inches =
`(60)/(12)=5\ feet.`

135 inches =
`(135)/(12)=11.25\ feet.`

Thus, the actual length of room is 5 feet and the actual width is 11.25 feet.

So, we put formula to get the actual area of the room by using formula:

`Area=length* width\\\\Area=5* 11.25\\\\Area=56.25\ square\ feet.`

Rounding the area in to whole number is 56 square feet.

Therefore, the area of the actual game room is 56 square feet.