Question

Lisa has three hog panels. Panel A is 8 feet long, panel B is 3 feet long, and panel C is 7 feet long. If the full length of each panel is used, can she build a triangular pen to hold her pet pig?


No, 8 - 7 < 3
Yes, 3 + 7 > 8
No, 3 + 7 < 8
Yes, 8 - 3 > 7

Answer 1

The side lengths of any two sides of a triangle must be greater than that of the third side (the triangle inequality). If this condition does not hold, then construction of a triangular pen is impossible.

If you attempt to arrange the 3 panels into a triangle, then you see that 3+7>8, 3+8>7, and 8+7>3.

Since all three inequalities hold, it is possible to build a triangle of the side lengths given. The answer would be the second one.