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Damm [24]
3 years ago
14

The lengths of two sides of a triangle are given below. Write an inequality to represent the range of the lengths of the 3rd sid

e.
4 and 10
Mathematics
1 answer:
KengaRu [80]3 years ago
6 0

9514 1404 393

Answer:

  6 < x < 14

Step-by-step explanation:

The shortest the third side can be is the difference between the given sides:

  10 -4 = 6

The longest the third side can be is the sum of the given sides:

  10 +4 = 14

So the inequality for side length x is ...

  6 < x < 14

__

<em>More detail</em>

These come from the triangle inequality, which requires ...

  a + b > c; b + c > a; c + a > b

Filling in 4, 10, and x, these become ...

  • 4 + 10 > x   ⇒   14 > x   . . . from the sum of the two given sides
  • 10 + x > 4   ⇒   x > -6 . . . . . less restrictive than the next
  • x + 4 > 10   ⇒   x > 6   . . . from the difference of the two given sides

In summary, 6 < x < 14.

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