Given triangle ABC with sides AB = 3x + 4 , BC = 2x + 5 , and AC = 4x , determine the values of x such that triangle ABC exists

Mathematics

1 answer:

Jlenok [28]3 years ago

8 0

Answer:

x > 1/5

Step-by-step explanation:

All of these three triangle inequalities must be satisfied:

AB +BC > AC

BC +CA > BA

CA +AB > CB

___

Taking these one at a time, we have ...

AB +BC > AC

3x +4 + 2x +5 > 4x

x +9 > 0 . . . . . subtract 4x

x > -9

BC +CA > BA

2x +5 + 4x > 3x +4

3x > -1 . . . . . . subtract 3x+5

x > -1/3 . . . . . divide by 3

CA + AB > CB

4x + 3x +4 > 2x +5

5x > 1 . . . . . . subtract 2x+4

x > 1/5

___

The only values of x that satisfy all of these inequalities are those such that ...

x > 1/5

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