Question

A new building is being constructed at UT Austin. It is 200 feet tall, and has a rectangular 100 ft by 150 ft footprint. The building has a walkway that is x feet surrounding all four sides of the building. If the total area (around and including the building) is 16,536 square feet, how wide is the walkway?

Answer 1

3 feet

Explanation:

You want the width of a uniform walkway around a 100 ft by 150 ft building such that the total area of the building and walkway is 16,536 square feet.

Setup

If the width of the walkway is x, the dimensions of the rectangle that includes the walk and the building are (100 +2x) by (150 +2x). It is that area that is 16,536 square feet:

(100 +2x)(150 +2x) = 16,536

Solution

Expanding the equation and putting it in standard form, we get ...

15000 +500x +4x² = 16536

4x² +500x -1536 = 0

x² +125x -384 = 0

(x +128)(x -3) = 0 . . . . . factor

x = 3 or -128

The negative solution is extraneous.

The walkway is 3 feet wide.

__

Additional comment

The area of a rectangle is the product of its dimensions:

A = LW