Discussion
The diagonal of a rectangle is thrice its smaller side. The ratio of the length to the breadth of the rectangle is
Answer: D
Let the smaller side be b and the diagonal d = 3b. The other side l satisfies \[l^{2}=d^{2}-b^{2}=9b^{2}-b^{2}=8b^{2},\] so \(l=2\sqrt{2}\,b\).
The ratio of length to breadth is \(2\sqrt{2}:1\), option D. The ratio \(3:1\) is diagonal to side, \(\sqrt{3}:1\) and \(\sqrt{2}:1\) do not satisfy the Pythagoras relation here.
Check with numbers: if the smaller side is 1, the diagonal is 3 and the larger side is the square root of 8, which is 2 times the square root of 2, so the ratio is 2.828 to 1.
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