# The distance from Arville to Branton is 114 miles. The distance from Branton to Camford is 247 miles. If the 3 towns form a triangle, what's therange of distances from Arville to Camford?

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In a triangle the sum of measures of any side is always less than the sum of other two sides.

As Arville, Bronton and Camford form a triangle, the distance between Arville to Camford must be less than the sum of distances of Branton from these two places. Thus

Distance between Arville to Camford < (Distance between Arville to Branton) + (Distance between Camford to branton)

==> Distance between Arville to Camford < 114 + 247

==> Distance between Arville to Camford < 361

The distance between Arville to Camford also must be more than the difference of distances of Branton from these two places. Thus

Distance between Arville to Camford > (Distance between Camford to Branton) - (Distance between Arville to Branton) +

==> Distance between Arville to Camford > 247 - 114

==> Distance between Arville to Camford > 133

Thus:

Distance between Arville to Camford must be more than 133 miles and less than 361 miles.

WE know that the three towns form a triangle.

For the formation of the three towns, the length of the 3 sides a, b and c shold be such that the grest side a < b+c, where b and c are the other two sides. If a is the smallest side, a>. |b-c|, the difference of the other two sides.

In the given case the distance betwen Arville to Camford is not known. We call this distance a.

Then by the above rule a < 247+114 = 361. Or

a < |247-114| = 133.

Therefore the range of the value of **a **the distance betweenAriville to Camford) is : 133 < a < 361.