Stephanie is bike-riding around her town. First she bikes to her friend's house, which is 2 miles west of her house. She then bikes to the deli, which is 2.5 miles southeast of her friend's house.
After that, she bikes north, directly back to her home. How many miles was her bike ride, in all?
2 miles
Friend's
House
Stephanie's
House
x miles
2.5 miles
Deli

Stephanie's bike ride in all is 6 miles

Step-by-step explanation:

The distance Stephanie rode her bike to her friend's house = 2 miles

The direction of Stephanie's friends house from her house = West

The distance Stephanie road to the deli South-East of her friend's house = 2.5 miles

Let 'x' represent the distance Stephanie bikes north back home from the deli

We have that Stephanie's path formed a right triangle

By Pythagoras's theorem, we have;

x = √(2.5² - 2²) = √2.25 = 1.5

x = 1.5 miles

Stephanie's bike ride in all  = (The distance Stephanie rode her bike to her friend's house) + (The distance Stephanie road to the deli South-East of her friend's house) + x

∴ Stephanie's bike ride in all  = 2 miles + 2.5 miles + 1.5 miles = 6 miles

Stephanie's bike ride in all = 6 miles

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