If the rectangular garden is 120' X 180' and the gardener wants to keep 19,836 square feet for flowers, what's the width of the path?

Answer 1

Draw and label a diagram!

w represents the width of the path

(120 - 2w)(180 - 2w) = 19836

Can you solve for w and answer?

Answer 2

Let w = with of path.

(180 - 2w)(120 - 2w) = 19836

This simplifies to (90 - w)(60 - w) = 4959

5400 - 150w + w^2 = 4959

w^2 - 150 w + 441 = 0

(w - 147)(w - 3) = 0

w = 3 feet (rejecting the obviously absurd and extraneous solution of 147)

You could also use the quadratic equation but I am an advocate of factoring whenever possible.

(If you are not sure whether the equation can be factored and you don't want waste a lot of time trying only to find out that it cannot be factored simply find b^2 - 4ac which in this case will be 150^2 - 4(1)(441) = 20736 and because that is a perfect square the solutions are rational and the equation can be factored. If it isn't you will have already done the major part of the work necessary to use the quadratic equation so it is a good 'investment' of about a minute of your time.)