Question

5. A w-foot wide path is to be built around a rectangular space that is 80

feet by 50 feet. Write and simplify an expression for the total area.

Answer 1

To find the area of the path, we'll need to find the area of the space with the path and subtract the area of the inner space.

Total area: (80 + w)(50 + w)

Inner area: 80 x 50

Area of the path: (80 + w)(50 + w) - (80 x 50)

(4000 + 80w + 50w + w^2) - (4000)

4000 + 130w + w^2 - 4000

w^2 + 130w

w(w + 130)

Expression for the total area: (80 + w)(50 + w)

Expression for the area of the path: w(w + 130)

Hope this helps!! :)