Is it possible to build a triangle with side lengths 7 9 12?

Answer 1

Yes, since 7+9 > 12. If you want to construct one, you need a compass (the kind that draws circles, not the one that tells North) and a ruler.

Measure off 12 units (centimeters, inches, etc.) Pick a point a and label it A, and draw a circle with 12 unit radius, using point A as the center.

Next, set the compass to 7 units, and using the same point A as the center, draw a 7 unit radius circle. Next, pick a point on the edge of the 12 unit circle, and label it B. Set the compass to 9 units, and draw a circle centered at B. Draw a line segment from A to B (this is the 12 unit side). Find where the 9 unit circle intersects the 7 unit circle (there will be 2 points of intersection). Label one of these two points as C. Draw a line segment from B to C; this is the 9 unit side. Draw a line segment from point A to C (this is the 7 unit side). On the related link, there is a JPEG of what this would look like.