If the sides of a triangle have the following lengths, AB = 2x + 5, BC = 3x-2 and AC = 4x - 8, find all the possible values of x

Question

2 years ago

15

.

1 answer:

katovenus [111] · Answer 1 · 2023-01-13T09:16:03+03:00

9514 1404 393

Answer:

x > 3

Step-by-step explanation:

The triangle inequality requires ...

AB +BC > AC

(2x +5) +(3x -2) > (4x -8)

5x +3 > 4x -8

x > -11

BC +AC > AB

(3x -2) +(4x -8) > (2x +5)

7x -10 > 2x +5

5x > 15

x > 3

AC +AB > BC

(4x -8) +(2x +5) > (3x -2)

6x -3 > 3x -2

3x > 1

x > 1/3

The most restrictive of these conditions on x is ...

x > 3 . . . . all possible values of x