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allsm [11]
2 years ago
11

A triangle has side lengths of 7 inches, 12 inches, and c inches. Enter values to write an inequality that describes the possibl

e values for c, the length of the third side of the triangle.
Mathematics
1 answer:
Leokris [45]2 years ago
6 0

<u><em>Answer:</em></u>

The inequality is: 5<c<19

Length of third side "c" can have values greater than 5 but less than 19

<u><em>Solution:</em></u>

Given that,

Length of two sides of triangle are 7 inches and 12 inches respectively

Let the length of third side be "c"

The Triangle Inequality Theorem, states that, the sum of the lengths of any two sides of a triangle is greater than the length of the third side

So we get a inequality as:

Case 1:

Sum of length of two sides of triangle > length of third side

Rewrite,

Case 2:

Let 12 inches be the length of third side

Sum of sides of length 7 and c > 12

Therefore from case 1 and case 2,

Which can be combined,

<u><em>Therefore the possible values of "c" are:</em></u>

<u><em>"c" can have values greater than 5 but less than 19</em></u>

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