Solved: A triangular plate made of homogeneous material has a constant thickness that is

Definitionb 1.1. Given two integers a and d with d non-zero, we say that d divides a (written d | a) if there is an integer c with a = cd. If no such integer exists, so d does not divide a, we write d - a. If d divides a, we say that d is a divisor of a. Proposition 1.2.1: Assume that a, b, and c are integers. If a | b and b | c, then a | c. Proposition 1.3. Assume that a, b, d, x, and y are integers. If d | a and d | b then d | ax + by. Corollary 1.4. Assume that a, b, and d are integers. If d | a and d | b, then d | a + b and d | a − b. Prime: A prime number is an integer p ≥ 2 whose only divisors are 1 and p. A composite number is an integer n ≥ 2 that is not prime. Ex: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. The Division Algorithm: Let a and b be integers with b > 0. Then there exist unique integers q (the quotient) and r (the remainder) so that a = bq + r with 0 ≤ r < b. The greatest common devisor: Assume that a and b are integers and they are not both zero. Then the set of their common divisors has a largest element d, called the greatest common divisor of a and b. We write d = gcd(a, b). 12: 1, 2, 3, 4, 6, and 12. 18: 1, 2, 3, 6, 9, and 18. Then {1, 2, 3, 6} is the set of common divisors of 12 and 18. Gcd(12,18) = 6 Proposition 1.10: If a and b are integers with d = gcd(a, b), then a b gcd , =1 . (d d The Division Algorithm: Let a and b be integers with b > 0. Then there exist unique integers q (the quotient) and r (the remainder) so tha