Question

(1) Every day, Gabrielle bicycles 3.6 miles due east from her house to school. After school, she bicycles due north from school to her friend Quinn's house, and then she bicycles home on a bike path that goes straight from Quinn's house to her own house. If the distance along the path from Quinn's house to Gabrielle's house is 8.9 miles, how far does Gabrielle bicycle each day? If necessary, round your answer to the nearest tenth. miles​

Answer 1

20.6 miles to the nearest tenth.

Explanation:

The 3 journeys form a right triangle with the hypotenuse equal to the length of the path from Quinn's house to Gabrielle's home.

By Pythagoras:

8.9^2 = 3.6^2 + x^2 where x is the distance from the school to Quinn's house.

x^2 = 8.9^2 - 3.6^2 = 66.25

x = √66.25

x = 8.14 miles

So the distance Gabrielle bikes each day

= 3.6 + 8.9 + 8.14

= 20.64 miles