https://file.aiquickdraw.com/mathbot/file/17260150492584cfntqs6.jpg

To solve the problem, let's consider the sides of the pentagon given in the image:

- Side \( AB = 8 \) yards
- Side \( BC = 6 \) yards
- Side \( CD = (-1 + x) \) yards
- Side \( DE = (2x) \) yards
- Side \( EF = 7 \) yards

The perimeter of the pentagon is the sum of all its sides, which is given as \( 37 \) yards.

Thus, we have the equation:

\[
8 + 6 + (-1 + x) + (2x) + 7 = 37
\]

Simplify and solve for \( x \):

\[
20 + x + 2x - 1 = 37
\]
\[
3x + 19 = 37
\]
\[
3x = 37 - 19
\]
\[
3x = 18
\]
\[
x = 6
\]

Now, substitute \( x = 6 \) back into the expressions for the sides:

- Side \( CD = -1 + x = -1 + 6 = 5 \) yards
- Side \( DE = 2x = 2(6) = 12 \) yards

So the side lengths are:

- \( AB = 8 \) yards
- \( BC = 6 \) yards
- \( CD = 5 \) yards
- \( DE = 12 \) yards
- \( EF = 7 \) yards

These sides sum up to the given perimeter:

\[
8 + 6 + 5 + 12 + 7 = 37 \text{ yards}
\]

Would you like more details on this solution or have any questions?

Here are some related questions:

1. What is the perimeter formula for a polygon with more sides?
2. How would the problem change if the perimeter was different?
3. What happens if one of the side lengths was expressed as a different function of \( x \)?
4. How would you solve this if the equation involved quadratic terms?
5. Can you explain how to verify a solution by recalculating with substituted values?

**Tip:** When solving for a variable in an equation that represents a sum of lengths, make sure all terms are correctly combined before isolating the variable.

Find the value of x and the indicated side lengths in a pentagon with the perimeter 37 yards. The side lengths are: AB = 8 yards, BC = 6 yards, CD = (-1 + x) yards, DE = 2x yards, and EF = 7 yards.

Learn how to solve for x and find the indicated side lengths in a pentagon with a perimeter of 37 yards. Side lengths are expressed in terms of x, and the solution involves algebraic simplification and perimeter calculation.

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