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.
Practise Edexcel A Level Maths 1.1 Proof by Contradiction with exam-style questions for A Level Maths. 100 questions, 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.