The formula for the perimeter $P$ of a rectangle is:

$P = 2l + 2w$

Where:

• $l$ is the length of the rectangle,
• $w$ is the width of the rectangle.

Given:

• The perimeter $P = 34$ units,
• The width $w = 6.5$ units.

Substitute the known values into the perimeter formula:

$34 = 2l + 2(6.5)$

Simplify:

$34 = 2l + 13$

Now, solve for $l$:

$34 - 13 = 2l$

$21 = 2l$

$l = \frac{21}{2} = 10.5$

Thus, the length of the rectangle is $10.5$ units.

Summary:

• The equation to determine the length is $34 = 2l + 2(6.5)$.
• The length of the rectangle is $l = 10.5$ units.

Would you like a more detailed explanation or help with another problem?

Related questions:

1. How do you calculate the area of a rectangle using the length and width?
2. What is the relationship between perimeter and area for different shapes?
3. How does changing the width affect the length of a rectangle with a constant perimeter?
4. How would you find the perimeter if the length and area of the rectangle are known?
5. Can the width of a rectangle ever be greater than the length if the perimeter is fixed?

Tip: Always check the units when solving perimeter or area problems to ensure consistency!