Question

Can the side lengths of 7, 10, and 9 form a triangle?

Answer 1

Answer: Yes a triangle can be formed.

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Step-by-step explanation:

• Add the first two sides to get 7+10 = 17 which is larger than the third side (9)
• Add the first and last sides to get 7+9 = 16 which is larger than the second side (10)
• Add the last two sides to get 10+9 = 19 which is larger than the first side (7)

As that list above shows, adding any two sides results in a sum larger than the third remaining side. The conditions of the triangle inequality theorem have been met to allow for a triangle to be formed.

In general the triangle inequality theorem is:

• a+b > c
• a+c > b
• b+c > a

The order doesn't matter. All that's important is that all three conditions are met.