Q:

A group of college students built a self-guided rover and tested it on a plane surface. They programmed the vehicle to move along the path A–B–C–D–A represented on the coordinate plane. What distance will the rover cover if it completes one circuit?A. 36 metersB. 40 metersC. 54 metersD. 60 metersE. 68 meters

Accepted Solution

A:
Answer: B. 40 metersStep-by-step explanation:— EstimatingThe rectangle enclosing the path has sides of length 9 m and 14 m, so its perimeter is 2(9+14) = 46 m. The distance covered will be shorter than that.The distance from A to C is longer than the distance from D to C, so we know the distance will be longer than 2·14+9 = 37 m.Only one answer choice fits in the range 37 < d < 46.____— Detailed calculationThe distance from B to C is the hypotenuse of a right triangle with sides 9 and 12. You will recognize that these side lengths are 3 times the side lengths of a 3-4-5 right triangle, so the hypotenuse distance is 3·5 = 15 meters.The circuit length is ... AB +BC +CD +DA = 2 + 15 + 14 + 9 = 40 . . . . meters