Question

Which of the following possibilities will form a triangle? Side = 15 cm, side = 6 cm, side = 8 cm Side = 15 cm, side = 6 cm, side = 9 cm Side = 16 cm, side = 9 cm, side = 6 cm Side = 16 cm, side = 9 cm, side = 8 cm

Answer 1

Answer:

Side = $16$ cm, side = $9$ cm, side = $8$ cm

Step-by-step explanation:

we know that

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

Applying the triangle inequality theorem

Verify each case

case A) Side = $15$ cm, side = $6$ cm, side = $8$ cm

$6+8 > 15$ ------> is not true

therefore

The possibility A) does not form a triangle

case B) Side = $15$ cm, side = $6$ cm, side = $9$ cm

$6+9 > 15$ ------> is not true

therefore

The possibility B) does not form a triangle

case C) Side = $16$ cm, side = $9$ cm, side = $6$ cm

$6+9 > 16$ ------> is not true

therefore

The possibility C) does not form a triangle

case D) Side = $16$ cm, side = $9$ cm, side = $8$ cm

$9+8 > 15$ ------> is true

$8+15 > 9$ ------> is true

therefore

The possibility D) forms a triangle

Answer 2

1) Side = 15 cm, side = 6 cm, side = 8 cm : NO, since there is one side that is  greater than the sum of the others, whereas it should SMALLER

2) Side = 15 cm, side = 6 cm, side = 9 cm : NO, since there is one side that is EQUAL to the sum of the others, whereas it should be smaller

3)Side = 16 cm, side = 9 cm, side = 6 cm :  NO, since there is one side that is GREATER than the sum of the others, whereas it should be smaller

4) Side = 16 cm, side = 9 cm, side = 8 cm : YES.