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.9 ft223 ft256 ft2270 ft

Answer 1

The scale factor from the drawing to the room is 1 to 30. Then, multiply the dimensions of the drawing by 30 to obtain the real dimensions of the room. Then, use the real values to find the area of the room.

Since the length is labeled 2 inches, the real length of the room is:

`2in*30=60in`

Since the width is labeled 4.5 inches, the real with of the room is:

`4.5in*30=135in`

1 foot is equal to 12 inches. Then, divide the dimensions by 12 to find the measurements in feet:

`\begin{gathered} 60in=60in*(1ft)/(12in)=5ft \\ \\ 135in=135in*(1ft)/(12in)=11.25ft \end{gathered}`

Multiply the width and the length to find the area of the room:

`A=(5ft)(11.25ft)=56.25ft^2\approx56ft^2`

Therefore, to the nearest whole number, the area of the game room is 56ft^2.