Question

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

Answer 1

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.