Math Problem Statement

Ana walks 6 blocks north and then 9 blocks west to get to her Grandmother's house. On the way home she decides to cut through the park to save time. Which is the best estimate for the distance she walked on the way home?

Solution

The problem asks for the best estimate of the distance Ana walked on the way home, cutting through the park, which forms a right triangle between her house and her grandmother's house.

In the image, Ana walks 6 blocks north and then 9 blocks west. The straight-line distance (hypotenuse) from her grandmother's house to her own house is the key question.

To solve this, we can use the Pythagorean theorem, which relates the sides of a right triangle:

c2=a2+b2c^2 = a^2 + b^2

Where:

  • a=6a = 6 (blocks north)
  • b=9b = 9 (blocks west)

Substituting the values:

c2=62+92=36+81=117c^2 = 6^2 + 9^2 = 36 + 81 = 117

c=11710.8c = \sqrt{117} \approx 10.8

So the best estimate of the distance she walked on the way home is approximately 11 blocks. Therefore, the correct answer is C. 11 blocks.

Would you like more details or have further questions?

Here are some related questions to explore:

  1. How would the distance change if Ana walked a different number of blocks north or west?
  2. What if Ana walked along a different path that didn't create a right triangle?
  3. How do you apply the Pythagorean theorem to other real-world scenarios?
  4. Can you think of another way to estimate the straight-line distance without using the Pythagorean theorem?
  5. What are the conditions where the Pythagorean theorem doesn't apply?

Tip: Always remember that the Pythagorean theorem only works for right-angled triangles!

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Math Problem Analysis

Mathematical Concepts

Pythagorean Theorem
Distance Measurement
Right Triangles

Formulas

c^2 = a^2 + b^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-8