A design engineer is specifying the dimensions of a rectangular metal brace for a heavy-duty storage rack. The width of the brace is W W\,W cm and the height is H H\,H cm, where W,H∈Z+W, H \in \mathbb{Z}^+W,H∈Z+. The diagonal length of the brace is D D\,D cm.
Provide a specific example of values for WWW, HHH, and D D\,D such that all three lengths are even integers.
By using proof by contradiction, show that it is impossible for W W\,W and H H\,H to both be odd integers if D D\,D is an integer.
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.