Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the outside of the triangle in such a way that the shortest distance of the dog from the triangle is exactly…
Question and options
Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the outside of the triangle in such a way that the shortest distance of the dog from the triangle is exactly 1 meter. The total distance covered (in meters) by the dog in one round is
Answer and explanation
Correct answer: B - \(19 + 2\pi\)
The path at distance 1 outside the triangle is made of the side lengths (4+6+9 = 19) plus circular arcs at the corners whose angles add up to 360 degrees, giving 2*pi*1. Total 19 + 2pi. 22 + 2pi wrongly uses 22 as the perimeter.
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