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Answer :
We are given the three side lengths of the triangle:
[tex]$$
\text{Side 1} = 5 - 2n \quad (\text{cm})
$$[/tex]
[tex]$$
\text{Side 2} = 7 + 10n \quad (\text{cm})
$$[/tex]
[tex]$$
\text{Side 3} = 8 - 9n \quad (\text{cm})
$$[/tex]
The perimeter [tex]$P$[/tex] of a triangle is the sum of the lengths of its sides. Therefore, we have:
[tex]$$
P = (5 - 2n) + (7 + 10n) + (8 - 9n)
$$[/tex]
Now, we will simplify the expression step-by-step.
1. Combine the constant terms:
[tex]$$
5 + 7 + 8 = 20
$$[/tex]
2. Combine the terms with [tex]$n$[/tex]:
[tex]$$
-2n + 10n - 9n = (-2 + 10 - 9)n = -n
$$[/tex]
3. Write the simplified expression:
[tex]$$
P = 20 - n
$$[/tex]
Thus, the expression that represents the perimeter of the triangle, in centimeters, is:
[tex]$$
\boxed{20 - n}
$$[/tex]
[tex]$$
\text{Side 1} = 5 - 2n \quad (\text{cm})
$$[/tex]
[tex]$$
\text{Side 2} = 7 + 10n \quad (\text{cm})
$$[/tex]
[tex]$$
\text{Side 3} = 8 - 9n \quad (\text{cm})
$$[/tex]
The perimeter [tex]$P$[/tex] of a triangle is the sum of the lengths of its sides. Therefore, we have:
[tex]$$
P = (5 - 2n) + (7 + 10n) + (8 - 9n)
$$[/tex]
Now, we will simplify the expression step-by-step.
1. Combine the constant terms:
[tex]$$
5 + 7 + 8 = 20
$$[/tex]
2. Combine the terms with [tex]$n$[/tex]:
[tex]$$
-2n + 10n - 9n = (-2 + 10 - 9)n = -n
$$[/tex]
3. Write the simplified expression:
[tex]$$
P = 20 - n
$$[/tex]
Thus, the expression that represents the perimeter of the triangle, in centimeters, is:
[tex]$$
\boxed{20 - n}
$$[/tex]
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