A structural engineer is designing a triangular support frame where the side lengths are p,qp, qp,q and rrr, with p,q,r∈Z+p, q, r \in \mathbb{Z}^+p,q,r∈Z+. The frame forms a right-angled triangle where rrr is the length of the hypotenuse, such that p2+q2=r2p^2 + q^2 = r^2p2+q2=r2.
State an example of a set of values for p,qp, qp,q and rrr such that they are all multiples of 10.
Prove by contradiction that it is impossible for both ppp and qqq to be non-multiples of 3 if rrr is a multiple of 3.
132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.