Question

17 A room in the shape of a right rectangular prism is 3 meters high and 1.5 times as long as it is wide. If the volume of the room is 4.5x cubic meters, what could x represent? A) The length of the room, in meters The width of the room, in meters The perimeter of the room's floor, in meters The area of the room's floor, in square meters B) C) D)

Answer 1

x represents the width of the room.

Explanation:

Given : A room in the shape of a right rectangular prism is 3 meters high and 1.5 times as long as it is wide.

Solution:

Height of rectangular prism = 3 m

Let the width of the rectangular prism be x

We are given that Length is 1.5 times width

So, Length of rectangular prism = 1.5x

Volume of rectangular prism =
`Length * Width * Height`

=
`1.5x * b * 3`

=
`4.5x^2`

Now we are asked what x represents

So, x represents the width of the room.

Hence x represents the width of the room, in meters .

Answer 2

The right question is as follows.

A room in the shape fo a right rectangular prism os 5 meters high and 1.5 times as long as it is wide. Ifthe volume of the room is 4.5x² cubic meters, what could x represent?

A) The length of the room, in meters.

B) The width of the room, in meters

C) The perimeter of the room's floor, in meters

D) The area of the room's floor, in square meters.

Answer: D) The area of the room's floor, in square meters.

Explanation: The volume of a right rectangular prism is calculated as:

V = area of base*height

and area of base, as it is a rectangle is: A = length.width

Length and width are x and 1.5x, respectively.

Area of base is: A = 1.5x*x = 1.5x²

Therefore, Volume is:

V = 1.5x²*3

V = 4.5x² m³

In conclusion, x represents the area in m², since every measurement is in that unit.