EXAMPLE 3.7.4

The diagram below shows the path the Plato takes when he goes for a philosophical stroll.

Plato starts at home, proceeds to the toga shop, then heads north to the tunic store, then returns home. On average, Plato thinks one profound thought for every 10 yards that he walks. Find the total number of profound thoughts that he will think during this walk.

A. 60

B. 10

C. 100

D. 258

E. None of these

SOLUTION

To find the number of profound thoughts, we must find the number of yards that he walks and then DIVIDE by ten (since there is one profound thought for every ten yards). To find the distance he walks we must add the lengths of all three sides of the right triangle. We know that one leg measures 240 yards and the hypotenuse measures 260 yards. Let L be the length of the other leg. According to the Pythagorean Theorem:

260 squared equals L squared plus 240 squared
67,600 equals L squared plus 57,600
67,600 minus 57,600 equals L squared
10,000 equals L squared
The square root of 10,000 equals L.
L = 100 yards.

The length of the second leg is 100 yards, so the total distance he walks is 240 + 100 + 260 = 600 yards. Thus the number of profound thoughts is 600 divided by 10 equals 60. The correct choice is A.