Jeff wants to form a garden that is in the shape of a triangle. He has two lengths of fence that are 19 feet long and 12 feet long. He says he will be able to form a triangular garden with a third length of fence that is 8 feet long. Is Jeff correct or incorrect in his reasoning? Explain.

Jeff is correct as he will be able to form a triangular garden composed of the three side lengths meets the requirements of the triangle inequality theorem.

Given 3 lengths of the triangular fence as ; 19 feets, 12 feets and 8 feets

Say :

a = 19 feets ; b = 12 feets ; c = 8 feets

According to the triangle inequality theorem ; ,the sum of any two sides of a triangle must be greater than the third side ;

(a + b) > c

(b + c) > a

(a + c) > b

(19 + 12) = 31 feets > 8 feets

(12 + 8) = 20 feets > 19 feets

(19 + 8) = 27 feets > 12 feets

The lengths of Jeff's triangle meets the conditions of the triangle inequality theorem.

Hence, Jeff is correct.

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Jeff is correct

Step-by-step explanation:

In a triangle sum of any two sides is always grater than the third side.

Let us apply above rule for the given measurements of the sides of the triangle and check whether they comply with it or not.

19 + 12 = 31 > 8

19 + 8 = 27 > 12

12 + 8 = 20 > 19

Thus, given measurements are satisfying the above rule. So, Jeff is absolutely correct in his reasoning.

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step-by-step explanation: