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A triangle has one side that measures 1 foot and another side that measures 20 inches. What are possible lengths of the third side? (Select all that apply.)
6 inches
13 inches
28 inches
36 inches​

Sagot :

Answer:

The correct options for the possible lengths of the third side are;

13 inches

28 inches

Step-by-step explanation:

The given lengths of two sides of the triangle are;

The length of one side of the triangle = 1 foot = 12 inches

The length of the other side of the triangle = 20 inches

The question can be solved by the triangle inequality theorem as follows;

A + B > C

B + C > A

A + C > B

Let the given sides be A = 12 inches and B = 20 inches

We have;

12 + 20 = 32 > C

Therefore, by the triangle inequality theorem, the third side, 'C', is less than 32 inches

Similarly, when C = 6 inches, we have;

A + C = 12 + 6 = 18 < B = 20

Therefore, the third side cannot be 6 inches

when C = 13 inches, we have;

A + C = 12 + 13 = 25 > B = 20

Therefore, the third side can be 13 inches

when C = 28 inches, we have;

A + C = 12 + 28 = 30 > B = 20

Therefore, the third side can be 28 inches

akposevictor

Based on the triangle inequality theorem, the possible lengths of the third side of the triangle are: 13 inches and 28 inches.

The Triangle Inequality Theorem

The triangle inequality theorem states that, sum of the length of any two sides of a given triangle = length of the third side.

Given the measures,

  • 1 ft = 12 iches
  • 20 inches

The possible third side must make the three set of numbers conform to the triangle inequality theorem.

Thus, for 13 inches, we have:

13 + 12 > 20; 12 + 20 > 13; 20 + 13 > 12

Also, for 28 inches, we have:

28 + 12 > 20; 12 + 20 > 28; 20 + 28 > 12

Therefore, based on the triangle inequality theorem, the possible lengths of the third side of the triangle are: 13 inches and 28 inches.

Learn more about triangle inequality theorem on:

https://brainly.com/question/26037134

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