Answer:
Step-by-step explanation:
- See the attached for missing part of the question
As we see each design comprises of entrance and exit - each one tile and:
- Design 1 has 1 row and 3 columns,
- Design 2 has 2 rows and 4 columns,
- Design 3 has 3 rows and 5 columns.
So design x has x rows and two more columns according the pattern we observe.
The number of tiles of design x is:
- x by (x + 2) and 2 more tiles
We can put it as equation to get 170 tiles and solve for x:
- x(x+2) + 2 = 170
- x² + 2x - 168 = 0
- x² - 12x + 14x - 168 = 0
- x(x - 12) + 14(x - 12) = 0
- (x + 14)(x - 12) = 0
- x = - 14 (discarded as negative root)
- x = 12 (the solution)
So this is a design 12
It has 12 rows, 14 columns, 1 entrance and 1 exit tiles, the total number is
