Question

Find the mean proportion between 18 and 32

Answer 1

SOLUTION

TO DETERMINE

The mean proportion between 18 and 32

EVALUATION

Let x be the mean proportion between 18 and 32

So by the given condition

18 : x = x : 32

$\displaystyle\implies \sf{ \frac{18}{x} = \frac{x}{32} }$

$\displaystyle\implies \sf{ {x}^{2} = 18 \times 32}$

$\displaystyle\implies \sf{ {x}^{2} = 9 \times \: 64}$

$\displaystyle\implies \sf{ x = \pm \: (3 \times 8)}$

$\displaystyle\implies \sf{ x = \pm \: 24}$

FINAL ANSWER

The required mean proportion between 18 and 32 is - 24 or + 24

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