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

1 < x < 7.5

Step-by-step explanation:

This problem can be solved using given below property of triangle.

Sum of two sides is always greater than third side of triangle.

Difference of two sides is always lesser than third side of triangle.

Given

sides length

6.5 units

3.5 units

Third side is 2.5 +  x

using the property, Sum of two sides is always greater than third side of triangle.

6.5 + 3.5 > 2.5 +x

=>10 >2.5 + x

=>2.5 + x< 10

=> x< 10 -2.5

=> x < 7.5

using the property, Difference of two sides is always lesser than third side of triangle.

6.5 - 3.5 >  2.5 +x

=>3.5 >  2.5 +x

=> 2.5 +x  > 3.5

=> x  > 3.5 - 2.5

=> x  > 1

combining both we have

1 < x < 7.5

out of the given option none is 1 < x < 7.5

hence, correct answer will be 1 < x < 7.5 and wrong option can be claimed by student.

the answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question