find the lengths of the sides of a triangle with vertices (0,0)(5,0)(5,12)
To find the lengths of the sides of a triangle with vertices (0,0), (5,0), and (5,12), we can use the distance formula.
The distance formula is given as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
1) Length of the side from (0,0) to (5,0):
d1 = sqrt((5-0)^2 + (0-0)^2)
d1 = sqrt(5^2 + 0^2)
d1 = sqrt(25 + 0)
d1 = sqrt(25)
d1 = 5
2) Length of the side from (5,0) to (5,12):
d2 = sqrt((5-5)^2 + (12-0)^2)
d2 = sqrt(0^2 + 12^2)
d2 = sqrt(0 + 144)
d2 = sqrt(144)
d2 = 12
3) Length of the side from (5,12) to (0,0):
d3 = sqrt((0-5)^2 + (0-12)^2)
d3 = sqrt(-5^2 + (-12)^2)
d3 = sqrt(25 + 144)
d3 = sqrt(169)
d3 = 13
Therefore, the lengths of the sides of the triangle are 5, 12, and 13.