OE


Remember the third side rule of triangles here, which is how to find possible lengths of the third side of a triangle when given the two other sides. The third side rule dictates that the length of the third side of a triangle must be greater than the difference, but less than the sum, of the length of the two known sides. In this particular problem, the two known sides are 4 and 7. The difference between 4 and 7 is 3, and the sum of 4 and 7 is 11, so the third side of the triangle must be greater than 3 and less than 11. This can be represented by the expression 3 < x < 11. Use these values to create a range for the possible perimeter of the triangle. If the third side of the triangle is 3, and the other two sides are 4 and 7, the perimeter is 3 + 4 + 7 = 14. If the third side of the triangle is 11, and the other two sides are 4 and 7, then the perimeter is 11 + 4 + 7 = 22. Because the third side of the triangle is greater than 3 and less than 11, the perimeter of the triangle must be greater than 14 and less than 22. This can be represented by the expression 14 < perimeter < 22. The only answer choices that fall in that range are (B), (C), and (D), which are the correct answers.