Final answer:
By setting up a proportion based on similar triangles, the rise for a 50 inch run on the staircase is calculated to be 32 inches, which corresponds to Option A.
Step-by-step explanation:
To find the rise of the staircase when the run is 50 inches, we can use the concept of similar triangles. The total staircase has a vertical rise of 96 inches and a horizontal run of 150 inches. If we want to find the rise when the run is 50 inches, we create a proportion:
96 inches (total rise) / 150 inches (total run) = x inches (rise for 50 inches) / 50 inches (run for 50 inches)
We can solve for x, which represents the rise for a 50 inch run:
96 / 150 = x / 50
Cross-multiply to find the value of x:
96 * 50 = 150 * x
4800 = 150x
Now, divide both sides of the equation by 150:
x = 4800 / 150
x = 32
Therefore, the rise when the run is 50 inches is 32 inches (Option A).