Question

Triangle A B C is shown. Side A B has a length of 12. Side B C has a length of x. Side A C has a length of 15. The value of x must be greater than ________.

Answer 1

Explanation:

Given that,

AB = 12

BC= X

AC = 15

Therefore, To form a triangle the difference between two sides should be lesser than the third side

So,

X should be greater than 15 - 12 = 3

X > 3

Answer 2

To determine the minimum value of x in triangle ABC, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In triangle ABC, side AB has a length of 12 and side AC has a length of 15. For x to be a valid side length, the sum of AB and BC must be greater than AC.

12 + x > 15

To find the minimum value of x, we subtract 12 from both sides:

x > 15 - 12

x > 3

Therefore, the value of x must be greater than 3 in triangle ABC.