Question

from her home, rita would have to walk 3 miles north to get to her friend aubrey’s house and 3 miles east to get to her friend eddie’s house. one day, rita walked from her home to eddie’s house. together, eddie and rita cut directly through the field that separated them from aubrey’s house. when they finished playing at aubrey’s, rita walked back home. in all, how far did rita walk? if necessary, round to the nearest tenth.
□ miles

Explanation:

Step1: Identify Rita's first leg

Rita walks 3 miles east to Eddie's house.
Distance: $3$ miles

Step2: Calculate field path distance

The path from Eddie's to Aubrey's forms the hypotenuse of a right triangle with legs 3 miles (north) and 3 miles (east). Use Pythagorean theorem: $c=\sqrt{a^2+b^2}$

$$ \sqrt{3^2 + 3^2} = \sqrt{9+9} = \sqrt{18} \approx 4.24 \text{ miles} $$

Step3: Identify final leg distance

Rita walks 3 miles south (back home from Aubrey's).
Distance: $3$ miles

Step4: Sum all walking distances

Add the three segments of Rita's journey.

$$ 3 + 4.24 + 3 = 10.24 $$

Step5: Round to nearest tenth

Round the total distance to one decimal place.

$$ 10.24 \approx 10.2 $$

Answer:

10.2 miles