Help with a word problem?

Question

Paul put a rectangular rug 18 feet long and 12 feet wide in his living room. A strip of flooring of uniform width can be seen around the rug. How wide is the strip if the area of the strip is 136 feet?

Answer 1

We know a couple of things here:

We can basically divide up the "strip" into 8 sections:
- 2 rectangular sections of length 18 and width w
- 2 rectangular sections of length 12 and width w
- 4 square sections of length and width w

We need to sum all of those areas up and get 136:

2 * 18 * w + 2 * 12 * w + 4 * w * w = 136
36w + 24w + 4w^2 = 136
60w + 4w^2 = 136
w^2 + 15w - 34 = 0
(w + 17)(w - 2) = 0
w = -17 or 2

Obviously, the width can't be -17 feet, so it must be 2 feet.

Answer 2

Jeremiah's answer is correct. Here's another way to think about it. The math will eventually work out the same.

Find the total area of the room as the area of the rug, plus the area of the strip: (18 x 12) + 136 = 352.

If the strip is x feet wide, then the length of the room is (18 + 2*x). The width is (12 + 2*x). Then, the total area of the room is (18 + 2x) * (12 + 2x).

From here, you'll get 4x^2 + 60x + 216 = 352, which simplifies to the same as Jeremiah.