Answer:
9 +√41 ≈ 15.4 units
Step-by-step explanation:
You want the perimeter of the triangle with vertices A(-1, 5), B(4, 5), and C(-1, 1).
Side lengths
Side AB is on the horizontal line y=5, so its length is the difference of the x-coordinates of those points:
AB = 4 -(-1) = 5
Side AC is on the vertical line x=-1, so its length is the difference of the y-coordinates of those points:
AC = 5 -1 = 4
Side BC is the hypotenuse of this right triangle with leg lengths 4 and 5. Its length is found using the Pythagorean theorem:
BC = √(AB² +AC²) = √(5² +4²) = √41 ≈ 6.4
Perimeter
The perimeter of the triangle is the sum of the lengths of its sides:
P = AB +AC +BC = 5 + 4 + √41
P = 9 +√41 ≈ 15.4 . . . . . units
