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The diagram shows three aid stations in a national park. Choose the values of x, y, and z that COULD represent the distances between the stations.
A) x = 7 miles, y = 8 miles, z = 18 miles
B) x = 4 miles, y = 7 miles, z = 12 miles
C) x = 5 miles, y = 9 miles, z = 14 miles
D) x = 8 miles, y = 12 miles, z = 15 miles

The diagram shows three aid stations in a national park Choose the values of x y and z that COULD represent the distances between the stations A x 7 miles y 8 m class=

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irspow
All possible triangles must obey the rule that the sum of any two sides must be greater than the third side...

Only D. is a possible combination of sides

Answer:

The correct option is D.

Step-by-step explanation:

The diagram shows three aid stations in a national park.

From the given graph it is clear that the three aid stations forms a triangle.

According to the properties of triangle the sum of two smaller sides is more than the larger side.

In option A, the given sides are x = 7 miles, y = 8 miles, z = 18 miles.

[tex]7+8=15<18[/tex]

Therefore the option A is incorrect.

In option B, the given sides are x = 4 miles, y = 7 miles, z = 12 miles.

[tex]4+7=11<12[/tex]

Therefore the option B is incorrect.

In option C, the given sides are x = 5 miles, y = 9 miles, z = 14 miles.

[tex]5+9=14[/tex]

Therefore the option C is incorrect.

In option D, the given sides are x = 8 miles, y = 12 miles, z = 15 miles.

[tex]8+12=20>15[/tex]

Here the sum of two smaller sides is more than the larger side. Therefore the option D is correct.

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