Question

Which collection of three side lengths can be used to form a triangle?

Answer 1

Hello!

In order to create a complete triangle, the sum of the two smaller sides must be greater than the largest side. This can be expressed using the following formula:

(S1) + (S2) > (S3)

We'll begin by inserting the first set of values into the inequality above:

3 + 6 > 10

Simplify the left side:

9 > 10

The inequality (9 > 10) is false. Therefore, the first set of values can be eliminated. Now complete the same process for the next set of values:

3 + 6 > 9
9 > 9

The inequality (9 > 9) is false. Therefore, we can eliminate the second set of values as well. Now complete the same process for the third set of values:

4 + 6 > 9
10 > 9

The inequality (10 > 9) is true. Therefore, we can confirm the third set of values (4 ft - 9 ft - 6ft) as a valid answer.

I hope this helps!