finding the width of a sidewalk

Question

Your neighborhood has just installed a new pool that measures 4 m by 9 m.

A sidewalk will surround the pool and its width will be uniform.

The area of the sidewalk will be 230 m2.

What is the width of the sidewalk?

Write the necessary equation and solve it

Answer 1

The width of the entire setup is is 4 + 2w, and the length is 9 + 2w, so the total area is (4+2w)(9 + 2w). The area of the sidewalk surrounding the pool would be the total area minus the area of the pool or

(4+2w)(9 + 2w) -36 = 230. Expanding and rearranging this to put into standard quadratic form yields

4w² + 26w -230 = 0. You can use your calculator to solve this using the quadratic formula:

w = -b ± √( b² - 4ac) / 2a I got one answer of w = 5m and a negative value which cannot be an answer.

Answer 2

Dotty

Draw a picture.

If the width is w then the pool + sidewalk will have dimensions (9+w) x ( 4 + w)

Area of pool is 4 x 9 = 36

So area of sidewalk = ( 9 + w) ( 4+w) - 36 = 230

So (9+w) (4+w) = 194

You can solve this by plotting y = (9+x) (4+x) - 194 on Desmos or TI-84 and finding x when it is zero

Or expand brackets

36 + 13x + x² - 194 = 0, so x² + 13x - 158 = 0, and use the quadratic formula or factorisation to solve this

Mike