how far would it be from eds house to the store if there were a direct route?

Question

to get to the store, ed leaves his house and drives 8 miles south. he then turns east and drives 5 more miles. At this point, he has to turn due south and drive another 4 miles. how far would it be from eds house to the store if there were a direct route?

Answer 1

From starting point he has traveled 12 miles south and 5 miles east.

 

These can be the lengths of a right triangle.

 

The direct path is the hypotenuse.

 

 

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

 

c^2 = 12^2 + 5^2 = 144 + 25 = 169

 

C^2 = 169

 

To solve for C, we will take the square root of both sides.

 

C = 13

 

 

If there was a direct route, Ed would travel 13 miles

Answer 2

While it may not be precise or pretty, a picture is worth a 1,000 words:

 

 House

    |

    |

    |

    |

    |

    |

    |

    |

     _ _ _ _ _

                 |

                 |

                 |

                 |

            Store

 

This makes a right (90°) triangle when a line is drawn from Ed's house directly to the Store.  One side is the total of 12 miles (south) and the other side is 5 miles (east).

 

The Pythagorean Theorem is quite useful for computing the length of the hypotenuse (the direct distance).

     c² = a² + b²

     c² = (12)² + (5)²

     c² = 144 + 25

     c² = 169

     c = 13 miles

 

This is one of the "Pythagorean triples" that you will see very often in test and homework problems because all three sides are integers.  Remember (5,12,13).