Final answer:
The lengths of the sides of triangle ABC are AB = √13, BC = √13, and AC = √26. We found these lengths using the distance formula, which is derived from the Pythagorean theorem.
Step-by-step explanation:
To find the length of each side of triangle ABC, we will use the distance formula which is derived from the Pythagorean theorem.
Length of AB
The length of side AB can be found using the coordinates of points A(0, 2) and B(2, 5). Applying the distance formula:
AB = √((x2 - x1)² + (y2 - y1)²)
AB = √((2 - 0)² + (5 - 2)²)
AB = √(4 + 9)
AB = √13
Length of BC
The length of side BC is found using the coordinates of points B(2, 5) and C(-1, 7):
BC = √((-1 - 2)² + (7 - 5)²)
BC = √(9 + 4)
BC = √13
Length of AC
For side AC using the coordinates of points A(0, 2) and C(-1, 7):
AC = √((-1 - 0)² + (7 - 2)²)
AC = √(1 + 25)
AC = √26
Therefore, the lengths of the sides of triangle ABC are as follows: AB = √13, BC = √13, AC = √26.