Question

Isosceles triangle ABC has vertices A(3,5) and B(3,-5).

If the perimeter of triangle ABC is 53, what is a possible x-coordinate for point C?

Enter your answer as a decimal rounded to the nearest hundredth if not an integer.

Answer 1

If AC = BC then C lies on the perpendicular bisector of AB, which is y = 0, so C = (x,0). AB = 10, and AC = BC = sqrt((x-3)^2 + 25). Perimeter: 10 + 2 sqrt((x-3)^2 + 25) = 53
=> sqrt((x-3)^2 + 25) = 21.5
=> (x-3)^2 = 437.25
=> x - 3 = ±√437.25 ≈ ±20.91053

Thus x ≈ 3 + 20.91053 = 23.91 or x ≈ 3 - 20.91053 = -17.91.

A possible x-coordinate is 23.91 (the other possible value is -17.91).