Question

Can you make a triangle with side lengths 3,7,12

Answer 1

Answer:

No

Step-by-step explanation:

The third side length has to be smaller than the sum of the other two sides

3+7 > 12

10 >12

We cannot make a triangle

Answer 2

Answer: No, it is not possible

To prove this, use a ruler to measure out 3 inches and 7 inches on a piece of paper. After marking the lengths, cut out strips of paper of those sizes. Then try to form a ruler using those two strips of paper and the ruler as the third side. You'll find the strips of paper come up short and a triangle cannot be made.

The triangle inequality theorem says that a triangle is only possible if and only if summing any two sides leads to a result larger than the third side. We see that 3+7 = 10 is not larger than 12, so this invalidates the triangle inequality theorem; therefore, making a triangle not possible with these side lengths.