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Sagot :
Using a linear function, it is found that the expression to find the perimeter of the composite figure made up of t triangles is:
- [tex]P(t) = 2t + 10[/tex]
What is a linear function?
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
What is the perimeter of a figure?
- The perimeter of a figure is the sum of all it's outside dimensions.
Researching the problem on the internet, it is found that:
- When the figure is made of 1 triangle, the perimeter is of 12, as it is an isosceles triangle with two dimensions of 5 and one dimension of 2.
- When the figure is made of 2 triangles, the perimeter is of 14. For 3 triangles, it is of 16, and so on...
- Hence, when the number of triangles changes by 1, the perimeter changes by 2, which means that the slope is [tex]m = 2[/tex], and the equation is:
[tex]P(t) = 2t + b[/tex]
When t = 1, P(t) = 12, hence, we can find b:
[tex]12 = 2 + b[/tex]
[tex]b = 10[/tex]
Hence, the expression is:
[tex]P(t) = 2t + 10[/tex]
To learn more about linear function, you can take a look at https://brainly.com/question/25823744
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