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Determine which set of numbers can be the lengths of the sides of a triangle.

Determine Which Set Of Numbers Can Be The Lengths Of The Sides Of A Triangle class=

Sagot :

BrainCube

Answer:

A) 13, 10, 16

Step-by-step explanation:

The Triangle Inequality Theorem will help you solve this question. 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.

The options that are given are:

  • A) 13, 10, 16
  • B) 1, 2, 3
  • C) 5.2, 11, 4.9
  • D) 208, 9, 219

Lets solve each one to figure out if they could be the lengths of a triangle.

A) 13, 10, 16.

We can write three inequalities to see if the lengths are true.

13 + 10 > 16

10 + 16 > 13

13+ 16 > 10

Solve each one.

23 > 16

26 > 13

29 > 10

According to the information above, the set of numbers from option A does  fit the Triangle Inequality Theorem. Therefore, they are possible lengths.

B) 1, 2, 3

Write three inequalities:

1 + 2 > 3

2 + 3 > 1

3+ 1 > 2

Solve each.

3 > 3

5 > 1

4 > 2

As you see, only two lengths fit the theorem, but the third side (3 > 3) does not. This set of lengths is not a possible set for a triangle.

C) 5.2, 11, 4.9

Write three inequalities:

5.2 + 11  > 4.9

4.9 + 11 > 5.2

5.2 + 4.9 > 11

Solve each.

16.2 > 4.9

15.9 > 5.2

10.1 > 11

As you see, only two sides lengths can repsent the lengths of a triangle but the third does not, so its not a possible set of lengths for a triangle.

D) 208, 9, 219

Write three inequalities:

208 + 9 > 219

219 + 9 > 208

208+ 219 > 9

Solve each.

217 > 219

228 > 208

427 > 9

Although two lengths fit the theorem, one length does not, so this a not a possible set of lengths.

In summary, only one set of lengths is possible for a triangle, with is A.

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