Find the lengths of the sides of a triangle with vertices: (0, 0), (5, 0), (5, 12).

graph
(1 point)
Responses

5, 12, 12
5, 12, 12

5, 5, 12
5, 5, 12

5, 12, 5
5, 12, 5

5, 12, 13
5, 12, 13

1 answer

To find the lengths of the sides of a triangle with the given vertices, we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the lengths of the sides:

Side 1: (0, 0) to (5, 0)
d1 = sqrt((5 - 0)^2 + (0 - 0)^2)
= sqrt(25 + 0)
= sqrt(25)
= 5

Side 2: (5, 0) to (5, 12)
d2 = sqrt((5 - 5)^2 + (12 - 0)^2)
= sqrt(0 + 144)
= sqrt(144)
= 12

Side 3: (5, 12) to (0, 0)
d3 = sqrt((0 - 5)^2 + (0 - 12)^2)
= sqrt(25 + 144)
= sqrt(169)
= 13

Therefore, the lengths of the sides of the triangle are 5, 12, and 13. The correct answer is 5, 12, 13.