The 3-4-5 rule for triangles states that if the lengths of the three sides of a triangle are in the ratio of 3:4:5, then the triangle is a right triangle. Let's check this for each of the given triangles.
a. For the triangle with sides of 10.5, 14, and 17.5, we need to check if 10.5/3 equals 14/4 and if that equals 17.5/5. In this case, all three ratios simplify to 3.5, therefore, triangle a follows the 3-4-5 rule.
b. For the triangle with sides of 21, 28, and 35, we need to check if 21/3 equals 28/4 and if that equals 35/5. All these ratios simplify to 7, thus, triangle b follows the 3-4-5 rule.
c. For the triangle with sides of 18, 24, and 36, we need to see if 18/3 equals 24/4 and if that equals 36/5. The first two ratios simplify to 6, but 36/5 simplifies to 7.2. Therefore, triangle c does not follow the 3-4-5 rule.
d. For the triangle with sides of 15, 20, and 25, we need to check if 15/3 equals 20/4 and if that equals 25/5. In this case, all three ratios simplify to 5, so, triangle d follows the 3-4-5 rule.
So, based on the 3-4-5 rule, the triangle c with sides 18, 24, and 36 does not conform to the rule and is therefore not a right triangle.