Question
A triangle is shown in the figure below. What is the perimeter? Units are inches. Round to the nearest inch.
R is (-9,6) S is (10,6) T is (10, -7)
Responses
49 in
51 in
57 in
55 in
R is (-9,6) S is (10,6) T is (10, -7)
Responses
49 in
51 in
57 in
55 in
Answers
GPT 3.5
To find the perimeter of the triangle, we need to calculate the distance between each pair of points and then sum them up.
The distance between R and S:
√((-9 - 10)^2 + (6 - 6)^2) = √(19^2) = 19 inches
The distance between S and T:
√((10 - 10)^2 + (6 + 7)^2) = √(7^2) = 7 inches
The distance between T and R:
√((10 + 9)^2 + (-7 - 6)^2) = √(19^2 + 13^2) = √(670) = 25.9 inches (rounded to the nearest inch, this is 26 inches)
Adding these distances together:
19 + 7 + 26 = 52 inches
Rounded to the nearest inch, the perimeter of the triangle is 52 inches. None of the provided responses are correct.
The distance between R and S:
√((-9 - 10)^2 + (6 - 6)^2) = √(19^2) = 19 inches
The distance between S and T:
√((10 - 10)^2 + (6 + 7)^2) = √(7^2) = 7 inches
The distance between T and R:
√((10 + 9)^2 + (-7 - 6)^2) = √(19^2 + 13^2) = √(670) = 25.9 inches (rounded to the nearest inch, this is 26 inches)
Adding these distances together:
19 + 7 + 26 = 52 inches
Rounded to the nearest inch, the perimeter of the triangle is 52 inches. None of the provided responses are correct.