Final answer:
The width of the similar ceramic tile, which has a length of 8.5 inches, is calculated to be 6 inches by using the scale factor determined from the plywood's dimensions.
Step-by-step explanation:
Finding the Width of a Similar Rectangular Tile
To find the width of the tile, we must first understand the concept of similar rectangles. Similar figures have the same shape but different sizes and are in proportion to each other. In this question, the ratio of the lengths is the scale factor, and it can be used to calculate the unknown width of the tile.
The larger piece of plywood has dimensions of 68 inches (length) by 48 inches (width). We're given the length of the similar tile as 8.5 inches. To find the corresponding width, we keep the ratios proportional:
Length of plywood: 68 inches Length of tile: 8.5 inches Width of plywood: 48 inches Width of tile: Let's call this w inches.
The ratio of the lengths is 68/8.5 which simplifies to 8/1. This is the scale factor. Let's set up a proportion using this scale factor:
68/8.5 = 48/w. Now, we cross-multiply to find the width of the tile:
68w = 8.5 * 48 68w = 408 w = 408/68 w = 6
So the width of the tile is 6 inches.