Bot GPT 4-o mini To find the direct route back home, we can use the Pythagorean theorem, which states:
\( a^2 + b^2 = c^2 \)
In Van's case, he walked 3 blocks south and 4 blocks west to get to the coffee shop. We can treat this situation as a right triangle where:
- One leg of the triangle (south) is 3 blocks (a = 3).
- The other leg of the triangle (west) is 4 blocks (b = 4).
Now, we can calculate the length of the hypotenuse (the direct route back home):
- Substitute \( a \) and \( b \) into the Pythagorean theorem:
\[ 3^2 + 4^2 = c^2 \]
- Calculate \( 3^2 \) and \( 4^2 \):
\[ 9 + 16 = c^2 \]
- Simplify the equation:
\[ 25 = c^2 \]
- So, taking the square root of both sides gives us:
\[ c = \sqrt{25} \]
- Therefore:
\[ c = 5 \]
So, the number of blocks Van will have to walk to get home from the coffee shop, taking the most direct route, is 5 blocks.
1 answer