Question

Right triangle ABC is shown below.

On a coordinate plane, a line goes through (1, 0) and (3, 5). A triangle has a rise of 5 and run of 2.

A similar right triangle would be created by a run of 8 and a rise of .

Answer 1

To find the rise of the similar right triangle that has a run of 8, we first need to determine the slope (or ratio of rise to run) of the original right triangle, which has a rise of 5 and a run of 2.

The slope of the original triangle is given by:

\[
\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{5}{2}
\]

For a similar triangle with a run of 8, we can use the same slope to find the corresponding rise. Let \( x \) be the rise for the triangle with a run of 8. We set up the equation using the slope:

\[
\frac{x}{8} = \frac{5}{2}
\]

To solve for \( x \), we can cross-multiply:

\[
2x = 5 \cdot 8
\]

\[
2x = 40
\]

Now, divide both sides by 2:

\[
x = \frac{40}{2} = 20
\]

Thus, the rise for the similar right triangle with a run of 8 is \( 20 \).

So, the final answer is:
\[
\text{Rise} = 20
\]