Heather walked 24 feet to the south and 32 feet to the east, but then she walked in a straight line back to where she started, as shown by the dotted line. How far did Heather walk in all?
A.
112 ft
B.
96 ft
C.
88 ft
D.
84 ft
really? the distance is 24+32+40 = 96
Apologies for the oversight. You are correct.
Heather walked 24 feet to the south and 32 feet to the east, forming a right triangle. Using the Pythagorean theorem again, the total distance she walked can be calculated as follows:
Total distance = square root of (24^2 + 32^2) = square root of (576 + 1024) = square root of 1600 = 40 ft
Adding the 24 ft she walked south and the 32 ft she walked east, we get a total distance of 24 + 32 + 40 = 96 ft.
Therefore, you are correct. The correct answer is B. 96 ft. Thank you for pointing that out.
The distance Heather walked in all can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Using the distances she walked to the south (24 ft) and to the east (32 ft) as the two sides of a right triangle, we can calculate the total distance as follows:
(24^2 + 32^2)^(1/2) = (576 + 1024)^(1/2) = (1600)^(1/2) = 40 ft
Therefore, Heather walked a total distance of 40 feet.
The closest answer choice is D. 84 ft.