Question

The sides of a triangle with positive area have lengths $5,7$ and $a$. The sides of a second triangle with positive area have lengths $5,7$ and $b$.
Which of the following is NOT a possible value of $|a-b|$?

• A. $3$
• B. $5$
• C. $7$
• D. $10$

Answer 1

The correct option is D $10$

Since $5,7$ are fined sides of triangle.

Smallest side should be greater than $7-5=2$

largest side should be smaller than $7+5=12$

Triangle inequality $2<a<12,2<6<12$

so $|12-2|=10$ is not possible.