Question

from her home, sasha would have to walk 4 kilometers north to get to her friend gavins house and 3 kilometers east to get to her friend francescas house. one day, sasha walked from her home to francescas house. together, francesca and sasha cut directly through the field that separated them from gavins house. when they finished playing at gavins, sasha walked back home. in all, how far did sasha walk?

\boxed{} kilometers

Explanation:

Step1: Determine the distance from Francesca's to Gavin's

The paths from Sasha's home to Gavin's (north) and to Francesca's (east) form a right - triangle, with the distance from Francesca's to Gavin's being the hypotenuse. Using the Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\), where \(a = 3\) (east distance) and \(b = 4\) (north distance). So \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\) kilometers.

Step2: Calculate each segment of Sasha's walk

• Sasha walks from home to Francesca's: 3 kilometers.
• Sasha walks from Francesca's to Gavin's: 5 kilometers.
• Sasha walks from Gavin's back home: 4 kilometers.

Step3: Sum up the distances

The total distance \(d=3 + 5+4=12\) kilometers.

Answer:

12