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 Algebraic Methods with exam-style questions for A Level Maths. 261 questions covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof, 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.
