To find the length of the rectangle, we can use the formula for the perimeter of a rectangle:

$P = 2l + 2w$

where:

• $P$ is the perimeter,
• $l$ is the length,
• $w$ is the width.

We are given:

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

Substitute the known values into the perimeter formula:

$34 = 2l + 2(6.5)$

Now, simplify:

$34 = 2l + 13$

Next, subtract 13 from both sides:

$34 - 13 = 2l$

$21 = 2l$

Now, divide both sides by 2 to solve for $l$:

$l = \frac{21}{2} = 10.5 \, \text{units}$

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

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Would you like more details on the steps or have any other questions? Here are 5 related questions you could explore:

1. What is the formula for the area of a rectangle?
2. How can you derive the formula for the perimeter of a rectangle from its dimensions?
3. How would the perimeter change if the width of the rectangle increased to 8 units?
4. What happens to the perimeter if both the length and the width are doubled?
5. How can we determine the length of a rectangle if we know its area and width?

Tip: Always remember to break down the problem step-by-step, especially with word problems. It often helps to translate the words into a mathematical equation first.