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A student states that a triangle can be formed with side lengths 3 in, 5 in, and 9 in. Is the student correct? Why, or why not?
O Yes, because 3 +5<9
O Yes, because 3 +9 > 5
O No, because 3+9>5
O No, because 3 + 5 <9

A student states that a triangle can be formed with side lengths 3 in 5 in and 9 in Is the student correct Why or why not O Yes because 3 5lt9 O Yes because 3 9 class=

Respuesta :

Answer:  Choice D.  No, because 3+5 < 9

Explanation: Refer to the triangle inequality theorem

This theorem states: a triangle is only possible if adding any two sides yields a sum larger than the third side.

In terms of inequalities, we need all 3 shown below to be true.

  • a+b > c
  • a+c > b
  • b+c > a

In this case, the triangle has sides a = 3, b = 5, c = 9

Notice how a+b = 3+5 = 8 is not larger than c = 9. Therefore, the inequality a+b > c is false to determine a triangle is not possible with these side lengths. Grab 3 pieces of string with lengths 3 inches, 5 inches, and 9 inches to try it out for yourself. The 3 inch and 5 inch pieces come up too short compared to the 9 inch side.

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