Question

If the diagonal length of a square is tripled, how much is the increase in the perimeter of that square ?

Answer 1

Let the square have sides lengths \(x\), then the perimeter is
\[P=4x\]
The ratio of diagonal length to side length is \(\sqrt2:1\), so the diagonal length is \(\sqrt2x\). Tripling the diagonal length gives a ratio of \(3\sqrt2:3\), so the side length is tripled. This makes the new perimeter three times larger:
\[P=4(3x)=12x\]
The difference between perimeters is \(12x-4x=8x\).