Question

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

Answer 1

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 2

The correct option is D.

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.

`7+8=15<18`

Therefore the option A is incorrect.

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

`4+7=11<12`

Therefore the option B is incorrect.

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

`5+9=14`

Therefore the option C is incorrect.

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

`8+12=20>15`

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