Question

Triangle DEF is rotated 90 degrees clockwise around the origin to create triangle D'E'F'.

If the perimeter of a triangle DEF is 24 inches, what is the perimeter of a triangle D'E'F'?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the perimeter of triangle D'E'F', we need to determine the lengths of the sides after the rotation.

Since the rotation is 90 degrees clockwise around the origin, the new coordinates of D, E, and F will be:
D' : (D.y, -D.x)
E' : (E.y, -E.x)
F' : (F.y, -F.x)

Let's assume the side lengths of triangle DEF are a, b, and c. Then, the side lengths of triangle D'E'F' will be:
D'E' = sqrt((E.y - D.y)^2 + (-E.x - (-D.x))^2) = sqrt((E.x - D.x)^2 + (E.y + D.y)^2) = sqrt(a^2 + b^2)
E'F' = sqrt((F.y - E.y)^2 + (-F.x - (-E.x))^2) = sqrt((F.x - E.x)^2 + (F.y + E.y)^2) = sqrt(b^2 + c^2)
F'D' = sqrt((D.y - F.y)^2 + (-D.x - (-F.x))^2) = sqrt((D.x - F.x)^2 + (D.y + F.y)^2) = sqrt(a^2 + c^2)

Therefore, the perimeter of triangle D'E'F' will be:
Perimeter = D'E' + E'F' + F'D' = sqrt(a^2 + b^2) + sqrt(b^2 + c^2) + sqrt(a^2 + c^2)

Given that the perimeter of triangle DEF is 24 inches, we can set a + b + c = 24. We need additional information about the side lengths of triangle DEF to calculate the exact perimeter of triangle D'E'F'.