If x, y and z are in continued proportion then show that $z : x :: z^{2} : y^{2}$ .

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Solution

If x, y, and z are in continued proportion then
$y^{2} = x z$ (1 Mark)
Multiply both sides of the equation by $z$
equation becomes,
$z y^{2} = x z^{2}$ (0.5 Marks)
$⟹$ $(z / x) = (z^{2} / y^{2})$ (0.5 Marks)
$⟹$ $z : x :: z^{2} : y^{2}$ (1 Mark)

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