Question

Fill in the blanks!

To get to the local coffee shop, Van left his house, walked 3 blocks south, and then walked 4 blocks west.

When he got to the coffe shop, Van realized he could take a more direct route home. How many blocks will Van have to walk to get home from the coffee shop if he takes the most direct route?

a^(2) + b^(2) = c^(2)
3^(2) + 4^(2) = c^(2)
_ + 16 = c^(2)
_ = c^(2)
(Underlined)+ \sqrt(25) = c
_ = c
5 blocks

Answer 1

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):

1. Substitute \( a \) and \( b \) into the Pythagorean theorem:

\[ 3^2 + 4^2 = c^2 \]

2. Calculate \( 3^2 \) and \( 4^2 \):

\[ 9 + 16 = c^2 \]

3. Simplify the equation:

\[ 25 = c^2 \]

4. So, taking the square root of both sides gives us:

\[ c = \sqrt{25} \]

5. 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**.