Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square.

To determine how much shorter Noam's walk would be if there were a direct path from the school to his house, we can apply the Pythagorean theorem.

### Step 1: Calculate the distance Noam currently walks
Noam walks 8 blocks north and 6 blocks east. The total distance he walks is:
\[
8 \text{ blocks} + 6 \text{ blocks} = 14 \text{ blocks}
\]

### Step 2: Calculate the direct distance using the Pythagorean theorem
If there were a direct path from the school to Noam's house, this would form the hypotenuse of a right triangle where the two legs are 8 blocks and 6 blocks.

The length of the direct path (hypotenuse \(c\)) can be found using:
\[
c = \sqrt{a^2 + b^2}
\]
where \(a = 8\) blocks and \(b = 6\) blocks.

\[
c = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \text{ blocks}
\]

### Step 3: Calculate how much shorter the direct path is
The difference between the current walk and the direct path is:
\[
14 \text{ blocks} - 10 \text{ blocks} = 4 \text{ blocks}
\]

### Final Answer
Noam's walk would be 4 blocks shorter if there were a direct path from the school to his house.

Would you like more details or have any questions? Here are some related problems to consider:

1. How long would it take Noam to walk home if he walks at a constant speed of 1 block per minute?
2. What would be the effect on the direct path distance if the number of blocks north was doubled?
3. If the blocks were rectangular instead of square, how would you calculate the direct distance?
4. How does the distance change if Noam first walks east and then north?
5. What would the distance be if Noam had to walk 10 blocks north and 12 blocks east?

**Tip:** When dealing with right triangles, the Pythagorean theorem is a powerful tool to determine the shortest distance between two points.

Learn how to calculate the shorter walk distance using the Pythagorean theorem. Noam walks 8 blocks north and 6 blocks east. Determine how much shorter his walk would be with a direct path from school to home. Explore step-by-step solution and related problems.

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