To solve this problem, we need to make sure all three ramps have the same slope. The slope of each ramp can be calculated by the formula:

$\text{slope} = \frac{\text{height}}{\text{base}}$

Given the table:

Step-by-Step Solution

1. Find the slope for Ramp 1:

   For Ramp 1: $\text{slope} = \frac{\text{height}}{\text{base}} = \frac{6}{8} = \frac{3}{4}$

2. Determine the values for Ramp 2 and Ramp 3 so that they have the same slope.

   • Ramp 2: Let the base of Ramp 2 be $x$. The height is given as 3.

     $\text{slope} = \frac{3}{x} = \frac{3}{4}$

     Solving for $x$:

     $3x = 4 \cdot 3 \implies x = 4$

     Therefore, the base of Ramp 2 is 4 feet.

   • Ramp 3: The base of Ramp 3 is given as 12. Let the height be $y$.

     $\text{slope} = \frac{y}{12} = \frac{3}{4}$

     Solving for $y$:

     $4y = 3 \cdot 12 \implies y = 9$

     Therefore, the height of Ramp 3 is 9 feet.

Final Table with Values

Would you like further details, or do you have any questions?

Related Questions to Explore

1. What is the formula for the slope of a line, and how is it derived?
2. How do slopes relate to similar triangles?
3. What other methods can be used to find missing sides of similar triangles?
4. How does changing the base or height affect the slope?
5. Can you find the slope for other triangles given different dimensions?

Tip

Always remember that triangles with the same slope are similar, meaning their corresponding angles are equal, and their corresponding sides are proportional.