You are the architectural technician for the firm designing a new building. You need to calculate the width for a parking lot that will surround a building based on customer specifications. The building that measures 90 m by 60 m is to be built on the lot and a paved parking lot of uniform width will surround the building. The paved lot is to have an area of 9000 m. Answer the questions that follow.
a) How wide is the paved area? Round to the nearest tenth of a metre.
Sir that's not nice
no trig needed here.
If the paved area has width w, then you know that
(90+2w)(60+2w) - 90*60 = 9000
To calculate the width of the paved area, we need to subtract the area of the building from the total area of the paved lot.
The area of the building is given by multiplying the length and width:
Area of the building = 90 m * 60 m = 5400 m^2
Now, subtract the building area from the total paved area to find the area of the paved lot:
Area of the paved lot = 9000 m^2 - 5400 m^2 = 3600 m^2
To find the width of the paved area, we'll divide the area by the length of the side adjacent to the parking lot. Since the parking lot surrounds the building on all sides, we can choose either the length or width of the building.
Divide the area of the paved lot by the length of the side adjacent to the parking lot:
Width of the paved area = Area of the paved lot / length of side adjacent to the parking lot
Since both the length and width of the building are given, you can choose either. Let's choose the length:
Width of the paved area = 3600 m^2 / 90 m = 40 m
Therefore, the width of the paved area is 40 meters.