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
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.
