Question

Carson uses cubes to make a pattern of shapes. The first shape has a height of

2 cubes and a length of 2 cubes, as shown below. For each step in the pattern,
Carson adds 1 cube to the height and I cube to the length. Which sentence
about the shapes in Carson's pattern is true?

Answer 1

Each shape in Carson's pattern will have its perimeter increased by 4 units each step as Carson adds 1 cube to both the height and the length, forming a rectangle whose sides grow by 1 unit each step.

Step-by-step explanation:

The true sentence about the shapes in Carson's pattern is that each shape will have a perimeter that increases by 4 units for each step. This is because each time Carson adds 1 cube to the height and 1 cube to the length, he is effectively adding 2 units to both the width (length) and the height of the rectangle, since each cube has a side length of 1 unit.

The original shape is a square with sides of 2 cubes each. This means the original perimeter is 2 units + 2 units + 2 units + 2 units = 8 units. For each additional cube added to the height and the length, the shape becomes a rectangle and the new perimeter is calculated as 2(height + 1) + 2(length + 1).

At each step, you are adding 2 units to the perimeter from the height and 2 units from the length, totaling an increase of 4 units in perimeter each time.

Answer 2

The length of each shape will alternate between even numbers and odd

numbers.​

Step-by-step explanation:

A cube is a 3 dimensional object that has equal length, width and height. It is has area of a cube.

Carson uses 2 cubes for the height and length for a start. He adds 1 cube to the length and height with respect to each stage. Since the length of each cube is the same, then consistent addition increases the length by same factor.

The length of each cube equals 1 unit, then he starts with 2 (length equals 2 units), next stage add 1 to make up 3(length equals 3 units). He add another 1 more for another stage to make up 4 (length equals 4 units)... This addition continues depending on the number of stages required.

Therefore, it can be deduced that the length of each shape will alternate

between even numbers and odd numbers.