Sure, let’s calculate the value of [tex]\( k \)[/tex] step by step.
1. Understand the Problem:
We are given two rectangles with the same area.
- The first rectangle has dimensions [tex]\( 3k \)[/tex] and [tex]\( 3 \)[/tex].
- The second rectangle has dimensions [tex]\( k+3 \)[/tex] and [tex]\( 6 \)[/tex].
2. Calculate the Area of Each Rectangle:
- For the first rectangle:
[tex]\[
\text{Area}_1 = \text{length}_1 \times \text{width}_1 = (3k) \times 3 = 9k
\][/tex]
- For the second rectangle:
[tex]\[
\text{Area}_2 = \text{length}_2 \times \text{width}_2 = (k + 3) \times 6 = 6(k + 3)
\][/tex]
3. Set Up the Equation:
Since the areas of both rectangles are the same, we can set up the equation:
[tex]\[
9k = 6(k + 3)
\][/tex]
4. Solve the Equation:
First, distribute the 6 on the right-hand side:
[tex]\[
9k = 6k + 18
\][/tex]
Next, isolate [tex]\( k \)[/tex] by subtracting [tex]\( 6k \)[/tex] from both sides:
[tex]\[
9k - 6k = 18
\][/tex]
Simplify the left-hand side:
[tex]\[
3k = 18
\][/tex]
Finally, solve for [tex]\( k \)[/tex] by dividing both sides by 3:
[tex]\[
k = \frac{3k}{3} = \frac{18}{3}
\][/tex]
Therefore:
[tex]\[
k = 6
\][/tex]
So, the value of [tex]\( k \)[/tex] is [tex]\( \boxed{6} \)[/tex].
