Question

Road Trip: Let's say two friends are meeting at a playground. Mary is already at the park but her friend Bobneeds to get there taking the shortest path possible. Bob has two way he can go - he can follow the roads gettingto the park - first heading south 3.miles, then heading west four miles. The total distance covered following theroads will be 7 miles. The other way he can get there is by cutting through some open fields and walk directly to"the park. If we apply Pythagorean theorem

Answer 1

5 miles

Step-by-step explanation

Let's draw the two possible paths Bob can take. One is walking 3 miles south and 4 miles west, and the other is walking in a straight line from where he is to the park,

If Bob takes the red path, the total distance he will travel is 7 miles. If he takes the blue path, the total distance he will travel can be found with the Pythagorean Theorem,

`c^2=a^2+b^2`

Solve for c taking the square root of both sides,

`c=√(a^2+b^2)`

Replace a and b, and solve,

`c=√(3^2mi^2+4^2mi^2)=√(9mi^2+16mi^2)=√(25mi^2)=√(25)mi=5mi`

Hence, the distance Bob will walk if he takes the blue path is 5 miles, which is the shortest path.