Question
Find the third proportional to $5.25, 7$

Answer

Let the required third proportional be $x$
$\therefore 5.25,7, x$ are in continued proportion
$\Rightarrow 5.25: 7=7: x $
$\Rightarrow 5 x=7 \times 7 $
$\Rightarrow x=\frac{7 \times 7}{5.25} $
$\Rightarrow x=\frac{49}{5.25}=\frac{28}{3} $
$\Rightarrow x=9 \frac{1}{3}$
$\therefore$ Required proportional $=9 \frac{1}{3}$

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