Calculate the width for a parking lot that will surround a building based on customer specifications.

Question

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^2.

a) How wide is the paved area? Round to the nearest tenth of a metre.

b.) What are the new dimensions for the lot?

Answer 1

The Area of the parking lot is the product of the new lot dimensions minus the area taken up by the building.

Uniform width means add x to all for sides of the building.

Area, A=(90+2x)(60+2x)-60(90)=9000

simplifying:

4x²+300x-9000 = 0

By quadratic equation, x = 22.9669, -97.9669 Choose the positive one and rounding, x=23

New lot dimensions are ≈ 106 m by 136 m.