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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

Road Trip Lets 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 Bo class=

Answer :

ANSWER

5 miles

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,

[tex]c^2=a^2+b^2[/tex]

Solve for c taking the square root of both sides,

[tex]c=\sqrt{a^2+b^2}[/tex]

Replace a and b, and solve,

[tex]c=\sqrt{3^2mi^2+4^2mi^2}=\sqrt{9mi^2+16mi^2}=\sqrt{25mi^2}=\sqrt{25}mi=5mi[/tex]

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

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