Let the length of the rectangle be $L$ and the width be $W$. According to the problem:

• The width is two-thirds of the length, so: $W = \frac{2}{3}L$

The perimeter $P$ of a rectangle is given by the formula: $P = 2L + 2W$

We're told the perimeter is 180 meters: $2L + 2W = 180$

Substitute $W = \frac{2}{3}L$ into the perimeter formula: $2L + 2 \times \frac{2}{3}L = 180$

Simplify the equation: $2L + \frac{4}{3}L = 180$

To eliminate the fraction, multiply the entire equation by 3: $3(2L) + 3\left(\frac{4}{3}L\right) = 3 \times 180$ $6L + 4L = 540$ $10L = 540$ $L = \frac{540}{10} = 54$

Now, substitute $L = 54$ into the equation for the width: $W = \frac{2}{3} \times 54 = 36$

Thus, the length of the rectangle is 54 meters and the width is 36 meters.

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Would you like further details or have any questions about this solution?

Here are 5 related questions to explore:

1. What is the area of the rectangle?
2. How would the perimeter change if the width was half the length instead of two-thirds?
3. What happens to the perimeter if both dimensions are doubled?
4. If the perimeter were 200 meters, what would the dimensions be?
5. How would you calculate the diagonal of the rectangle?

Tip: When dealing with relationships between dimensions, always express one variable in terms of the other to simplify solving for unknowns.