A sequence of figures is formed using tiles. Each tile is an equilateral triangle with side length 7 cm. The first figure consists of 1 tile. Each figure after the first is formed by adding 1 tile to the previous figure. The first four figures are as shown:
How many tiles are used to form the figure in the sequence with perimeter 91 cm?
The first figure consists of one tile with perimeter . Each time an additional tile is added, the perimeter of the figure increases by 7 cm (one side length of a tile), because one side length of the previous figure is “covered up” and two new side lengths of a tile are added to the perimeter for a net increase of one side length (or 7 cm). [[IMAGE0]] Since the first figure has perimeter 21 cm and we are looking for the figure with perimeter 91 cm, then the perimeter must increase by . Since the perimeter increases by 7 cm when each tile is added, then tiles need to be added to reach a perimeter of 91 cm. In total, this figure will have tiles.