Geometry problem solving paper

[tabithomp]

The road connecting the towns of Kings, Chana, and Holcomb form a triangle. Davis Junction is located in the interior of this triangle. The distances from Davis Junction to Kings, Chana, and Holcomb are 3km, 4km, and 5km, respectively. Jane begins at Holcomb and drives directly to Chana, then to Kings, and then back to Holcomb. At the end of her trip, she figures she has traveled 25km altogether. Has she figured the distance she traveled correctly?
1. Draw a diagram of the four towns.
2. The distance from Holcomb to Chana must be less than what distance?____km
3. The distance from Chana to Kings must be less then what distance?_______km
4. The distance from Kings to Holcomb must be less than what distance?______km
5. Jane must have traveled less than_________km.
6. Was Jane's calculated distance of 25 km correct? yes or no

 

[soroban]

Hello, tabithomp!

You are expected to be familiar with the "Triangle Inequality":
. . The sum of any two sides must be greater than the third side.

The road connecting the towns of Kings, Chana, and Holcomb form a triangle.
Davis Junction is located in the interior of this triangle.
The distances from Davis Junction to Kings, Chana, and Holcomb are 3km, 4km, and 5km, respectively.

Jane begins at Holcomb and drives directly to Chana, then to Kings, and then back to Holcomb.
At the end of her trip, she figures she has traveled 25km altogether.
Has she figured the distance she traveled correctly?

1. Draw a diagram of the four towns.
2. The distance from Holcomb to Chana must be less than what distance? __ km
3. The distance from Chana to Kings must be less then what distance? __ km
4. The distance from Kings to Holcomb must be less than what distance? __km
5. Jane must have traveled less than __km.
6. Was Jane's calculated distance of 25 km correct? .yes or no

                      C
                      o
                    * **
                  *  4* *
                *     *  *
              *      Do   *
            *     *     *  *
          *   *5         3* *
        * *                 **
    H o   *   *   *   *   *   o K

From the Triangle Inequality, we have: .\(\displaystyle \begin{array}{ccc}HC\,<\,9\;\;(2) \\ CK \,<\,7\;\;(3) \\ KH\,<\,8\;\;(4)\end{array}\)

Hence: \(\displaystyle HC\,+\,CK\,+\,KH\:<\:24\;\) (5)

(6) .No