Question

Mr. Cayetano plans to install a new exhaust fan on his room's square-shaped wall. He asked a carpenter to make a square opening on the wall where the exhaust fan will be installed. The square opening must have an area of 0.25 m2. Suppose the area of the remaining part of the wall after the carpenter has made the square opening is 6 m2. How big is the original square-shaped wall? Please provide the dimensions of the square wall.

Answer 1

The original square-shaped wall was 2.5 meters by 2.5 meters, with a total area of 6.25 m² including the area for the exhaust fan opening.

Step-by-step explanation:

Mr. Cayetano wants to install a new exhaust fan on his room's square-shaped wall. To fit the fan, a square opening with an area of 0.25 m2 is required. After this opening is created, the remaining wall area is 6 m2. To find the original size of the wall, we need to add the area of the opening to the remaining area.

The total wall area is:

0.25 m2 (area of the opening) + 6 m2 (remaining area) = 6.25 m2

To find the dimensions of the original square wall, we must find the square root of the total area:

√(6.25 m2) = 2.5 m

Therefore, the wall was originally 2.5 meters by 2.5 meters.