Final answer:
To calculate the perimeter of triangle RST, the distances of sides RS, ST, and RT are computed using the distance formula and then summed. Sides RS, ST, and RT are 24, 13, and 13 units long, respectively, making the total perimeter 50 units.
Step-by-step explanation:
The student has asked for the perimeter of triangle RST with given vertices R(-7,5), S(17,5), T(5,0). To find the perimeter, we must calculate the lengths of sides RS, ST, and RT using the distance formula, which is √((x₂-x₁)² + (y₂-y₁)²). After calculating each side, we add them all together to get the total perimeter.
For side RS, both points lie on the same horizontal plane (y=5), so the distance is simply the difference in the x-values: |17 - (-7)| = 24.
For side ST, we use the distance formula since these points do not share the same x or y values:
√((17-5)² + (5-0)²) = √(144 + 25) = √(169) = 13.
Finally, for side RT, we apply the distance formula again: √((-7-5)² + (5-0)²) = √(144 + 25) = √(169) = 13.
The perimeter (P) of triangle RST is the sum of the lengths of sides RS, ST, and RT: P = 24 + 13 + 13 = 50.
Therefore, the correct answer is B. 50.