Question

Which inequality represents the values of x that ensure triangle ABC exists? a triangle with side lengths of 6.5 units, 3.5 units, and 2.5 + x units A. 0.5 < x < 7.5 B. 3.0 < x < 7.5 C. -0.5 < x < 7.5 D. -3.0 < x < 7.5

Answer 1

Answer:

D. -3.0 < x < 7.5

Step-by-step explanation:

Given the side lengths of a triangle: 6.5 units, 3.5 units, and 2.5 + x units

For the triangle to exist:

• A side length cannot be negative
• A side length cannot be zero

Therefore, the third side length

x+2.5>0

x>-2.5

x must be greater than -2.5 and less than or equal to 6.5 units.

The correct option is D which satisfies this condition.

D. -3.0 < x < 7.5