Finding the width of a strip.

Question

A rug is to cover 2/3 of the floor area of a 14' by 18' room. The uncovered part of the floor forms a uniform strip around the rug. Find the width of the strip.

Answer 1

Hi Drew:

Here's how to tackle this type of question.

First, always draw a clear diagram (very important!)

Here, we have a smaller rectangle (the rug) inside a larger one (the floor) with a constant width strip around the rug. Let the width of the strip be x.

Then, the rug has dimensions (14 - 2x) and (18 - 2x). Can you see why?

And we are told that area of rug = 2/3 area of floor

=> (14 - 2x)(18 - 2x) = 2/3 (14 x 18)

252 - 64x + 4x² = 168

4x² - 64x + 84 = 0

x² - 16x + 21 = 0

Solve for x using the quadratic formula.