Concept explainers
For each diagram, find the relationship between the number of shapes and the perimeter of the figure they form. Represent this relationship using a table, words, an equation, and a graph.
To Fill: The table for perimeter for squares n.
Answer to Problem 2P
Explanation of Solution
Given information: 1 square has 4 units as perimeter, 2 squares has 6 units and 3 squares has 8 units and so on.
Calculation:
If we see the difference of y values they are increasing by 2 while x values are increasing by 1.
So, we can fill the next three boxes by increasing 2 from it’s previous value.
Now, let’s find the number of squares which has 22 as it’s perimeter.
Let’s continue the rule
Number of squares | Perimeter |
7 | 16 |
8 | 18 |
9 | 20 |
10 | 22 |
Now, let’s find the rule.
Take two points on the table and find the rule
(1,4) (3,8)
Slope
Plug in this value into
It gives
Using (1,4)
Subtract both sides 2
The rule is
Here, we need to use variable ‘ n’ for ‘ x’.
So, the rule is
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