SOLUTION: A triangle has sides measuring 5 inches and 12 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x?

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Question 1202681: A triangle has sides measuring 5 inches and 12 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x?
Found 3 solutions by Theo, math_tutor2020, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the length of the third side will be less than the sum of the first two sides.
the length of the third side will be greater than the absolute value of the difference between the first two sides.
the sum of the first 2 sides is 5 + 12 = 17
the absolute value of the differrence of the first 2 sides is |5 - 12| = |-7| = 7.
you get 7 <= x <= 17.
x is the length of the third side.

from the web:
The length of the third side of a triangle must always be between (but not equal to) the sum and the difference of the other two sides.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

a = 5
b = 12
c = x = unknown

Use the triangle inequality theorem to say:
b-a < c < b+a
12-5 < x < 12+5
7 < x < 17

Therefore, x is between 7 and 17 excluding both endpoints.
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.

The triangle inequality


    12 - 5 < x < 12 + 5,

or

    7 inches < x < 17 inches.    ANSWER

Solved.

-------------------------------

The answer in the post by @Theo

7 <= x <= 17

is incorrect. For such answer, a teacher gives a solid two on a five-point scale.



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