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bezimeni [28]
3 years ago
13

Which inequality represents the value of x that ensures triangle abc exists?

Mathematics
1 answer:
olasank [31]3 years ago
3 0

Answer:

Option A.

Step-by-step explanation:

According to triangle inequality theorem, a triangle exists if the sum of two sides is greater that third side.

Apply this theorem on each combination.

Case I: (2x+4)+6x>18

8x+4>18

8x>14

x>\dfrac{14}{8}

x>\dfrac{7}{4}      ...(1)

Case II: (2x+4)+18>6x

2x+22>6x

22>4x

\dfrac{22}{4}>x

\dfrac{11}{2}>x     ...(2)

Case III: 6x+18>2x+4

6x-2x>4-18

4x>-14

x>-\dfrac{14}{4}

x>-\dfrac{7}{2}     ...(3)

On combining (1), (2) and (3), we get

\dfrac{7}{4}

Therefore, the correct option is A.

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