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.
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
