Write and solve an equation to find the unknown side length $ I $ (in inches).

Given:
- Perimeter = 24.2 in
- Side 1 = 8.3 in
- Side 2 = 3.8 in
- Side 3 = 8.3 in

An equation is:

A. $ I + 8.3 + 3.8 + 8.3 = 24.2 $
B. $ I + 8.3 - 3.8 - 8.3 = 24.2 $
C. $ I + 8.3 + 3.8 - 8.3 = 24.2 $
D. $ I + 8.3 + 3.8 + 8.3 = 48.4 $

The correct equation to find the unknown side I is I + 83 + 3.8 + 83 = 24.2 in, but solving results in a negative side length, -145.6 inches, suggesting a potential typo in the given information. Retrying with a corrected total perimeter of 48.4 inches also yields a negative side length of -121.4 inches. Verification of the input data is required.

To solve for the unknown side length I of a polygon with a given perimeter, we use the perimeter formula which is the sum of all the side lengths. In this case, the perimeter is 24.2 inches, and it's given that the other three sides are 83 inches, 3.8 inches, and 83 inches long. The correct equation is option a) which adds the lengths of all the known sides and the unknown side I to make the total perimeter.

Equation: I + 83 + 3.8 + 83 = 24.2

Solving for I:

First, add the known side lengths: 83 + 3.8 + 83 = 169.8 inches
Second, subtract the sum of the known sides from the total perimeter: 24.2 - 169.8 = -145.6 inches
The result is a negative number, which indicates there might be a typo in the given dimensions or total perimeter, as side lengths cannot be negative.

However, if we consider the possibility of a typo in the total perimeter, and it should be doubled (48.4 inches) as in option d), then:

Solving for I with the corrected total perimeter:

Subtract the sum of the known sides from the corrected total perimeter: 48.4 - 169.8 = -121.4 inches, still a negative number.
It is essential to double-check the given values to ensure they are correct before solving the equation.

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