Eric has a straight garden path which is 2' x 15'. He wants to cover it with tiles that are each 1' x 2'.How many ways can he do this?
The 2' length of each tile will cover the width of the path. How many 1' widths are needed for the length of the path?
15
15.
Eric has a straight garden path which is 2' x 15'. He wants to cover it with tiles that are each 1' x 2'.HOW MANY WAYS CAN HE DO THIS?
To find the number of ways Eric can cover his garden path with the given tiles, we need to determine the number of arrangements possible.
Let's break down the problem step by step:
1. Determine the size of the garden path and the tiles:
- The garden path dimensions are 2' x 15'.
- The individual tiles are 1' x 2'.
2. Calculate the number of tiles needed to cover the garden path:
- Since the garden path is 2' wide, Eric would need 15 tiles to cover the width (15/1 = 15 tiles).
- Since the garden path is 15' long, Eric would need 7.5 tiles to cover the length (15/2 = 7.5 tiles). However, since tiles cannot be divided, we round up to the nearest whole number. So, Eric would need 8 tiles to cover the length.
3. Determine the number of ways Eric can arrange the tiles:
- Eric needs 15 tiles to cover the width and 8 tiles to cover the length.
- The number of ways to arrange these tiles can be calculated using combinatorics or permutations.
- Since the tiles on the width and length are independent, we can multiply the number of ways for each dimension.
- The number of ways to arrange 15 tiles in a 2-foot space can be calculated as 15!/(15-15)! = 1.
- The number of ways to arrange 8 tiles in a 15-foot space can be calculated as 8!/(8-8)! = 1.
- Thus, the total number of ways Eric can cover his garden path with the given tiles is 1 x 1 = 1.
Therefore, Eric can cover his straight garden path with tiles in only one way.