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\(\square\)ABCD is a rectangle. Write two simultaneous equations using information given below in the diagram, in the form of \(ax + by = c\) :[Figure: Rectangle ABCD with vertices A (top left), B (top right), C (bottom right), D (bottom left). Side…

Q.2 (B)(i) \(\square\)ABCD is a rectangle. Write two simultaneous equations using information given below in the diagram, in the form of \(ax + by = c\) :

[Figure: Rectangle ABCD with vertices A (top left), B (top right), C (bottom right), D (bottom left). Side AB is labelled \(2x + y + 8\), side BC is labelled \(x + 4\), side CD is labelled \(4x - y\) and side DA is labelled \(2y\).]

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Answer: \(2x - 2y = 8\) and \(x - 2y = -4\)

Opposite sides of a rectangle are equal.

AB = CD: \(2x + y + 8 = 4x - y \Rightarrow 2x - 2y = 8\)

BC = AD: \(x + 4 = 2y \Rightarrow x - 2y = -4\)

So the two equations are \(2x - 2y = 8\) and \(x - 2y = -4\) (solving them gives \(x = 12\), \(y = 8\), so each side is 40 units and 16 units).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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