John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.

Question

Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?

w(w – 2) = 48
w(w + 2) = 48
2w(w – 2) = 48
2w(w + 2) = 48

Answer 1

To create a rectangular mosaic where the length is 2 centimeters longer than the width (w), we can denote the width of the mosaic as \( w \) and the length as \( w + 2 \). The area of the rectangle (which must equal the total area of the tiles) is given by

\[ \text{Area} = \text{length} \times \text{width} = (w + 2) \times w. \]

Since John has 48 square centimeters worth of tiles, we set the area equal to 48:

\[ w(w + 2) = 48. \]

This equation represents the area of the rectangle in terms of its width. Thus, the correct equation that John can solve to find the greatest width \( w \) is:

\[ w(w + 2) = 48. \]