Question

the flower bed problem
anthony chens family operates a full - service pool and landscaping business. sometimes their clients want low decorative
fences around their flower beds.
anthonys father wants a quick way to estimate the amount of fencing needed. mr. chen asked anthony to help him. anthony
realizes that this is just a perimeter question.
he starts his task by analyzing the relationship between the length of the side of a square flower bed and the perimeter of the
flower bed. this will tell him the amount of fence needed to enclose the flower bed. anthony realizes that lengths of sides of
flower beds are not always whole numbers, but he decides to use square tiles to build models of flower beds of various sizes to
help him find a pattern. in his models, 1 tile represents 1 square foot.

1. draw the next two models in anthonys concrete representation next to the models shown.

Explanation:

Step1: Analyze the pattern of the given models

The first model has \(1\times1 = 1\) tile, the second has \(2\times2=4\) tiles, and the third has \(3\times3 = 9\) tiles. The side - length of the square (in terms of the number of tiles) is \(n\), and the number of tiles is \(n^{2}\).

Step2: Draw the next two models

For \(n = 4\), the model will be a \(4\times4\) square of tiles. For \(n=5\), the model will be a \(5\times5\) square of tiles.

Answer:

The fourth model is a \(4\times4\) square of tiles (16 tiles arranged in 4 rows and 4 columns) and the fifth model is a \(5\times5\) square of tiles (25 tiles arranged in 5 rows and 5 columns).