Question

Maria skates 40 feet due south in a skating rink. Then she skates 60 feet due east. Maria then skates diagonally across the ring back to where she started. What is the total distance, to the nearest foot, maria skates.

Answer 1

172 ft

Explanation:

Due south and due east form a 90-degree angle.

Her path is a right triangle. The 60 ft and 40 ft distances are the legs of the right triangle. We can use the Pythagorean theorem to find the hypotenuse. Then we add the lengths of the three sides to find the total distance she traveled which is the perimeter of the right triangle.

a^2 + b^2 = c^2

(40 ft)^2 + (60 ft)^2 = c^2

1600 ft^2 + 3600 ft^2 = c^2

c^2 = 5200 ft^2

c = 72 ft

perimeter = a + b + c = 40 ft + 60 ft + 72 ft = 172 ft

Answer 2

Answer: total distance is 172 feet

Explanation:

The different directions along which Maria moved forms a right angle triangle.

The diagonal distance, h across the ring back to where she started represents the hypotenuse of the right angle triangle. The distances due south and east represents the opposite and adjacent sides of the right angle triangle.

To determine h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

h² = 60² + 40²

h² = 5200

h = √5200

h = 72 feet

The total distance, to the nearest foot, maria skates is

72 + 60 + 40 = 172 feet