To determine which option correctly applies a Pythagorean triple for the 41 yards northwest route from Bessie's home to her school, we need to consider the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (in this case, 41 yards), and \( a \) and \( b \) are the legs of the right triangle formed by moving north and west.
Let's first calculate \( c^2 \):
\[ 41^2 = 1681 \]
Now we can examine each option to see if they satisfy the equation \( a^2 + b^2 = 1681 \).
-
Option 1: 9 yards north and 32 yards west
- \( 9^2 + 32^2 = 81 + 1024 = 1105 \) (not 1681)
-
Option 2: 12 yards north and 39.2 yards west
- \( 12^2 + 39.2^2 = 144 + 1536.64 = 1680.64 \) (not 1681, but very close)
-
Option 3: 12 yards north and 29 yards west
- \( 12^2 + 29^2 = 144 + 841 = 985 \) (not 1681)
-
Option 4: 9 yards north and 40 yards west
- \( 9^2 + 40^2 = 81 + 1600 = 1681 \) (this works)
The only option that correctly applies the Pythagorean theorem with \( a^2 + b^2 = c^2 \) for Bessie's route to school is:
9 yards north and 40 yards west.