Question

Find the third proportional to
$5\frac{1}{4},7$

Answer 1

$5\frac{1}{4},7$
Let the third proportional to $5\frac{1}{4},7$ be $x$
Then $5\frac{1}{4},7$ and $x$ are in continued proportion
i.e, $5\frac{1}{4},7::7:x$
$\frac{21}{4}:7::7:x$
Using the cross product the rule
Product of extremes =Product of means
$\frac{21}{4}\times x=7\times 7$
$\frac{21}{4}\times x=49$
$x=49÷\frac{21}{4}$
$x=49\times \frac{4}{21}$
$x=\frac{196}{21}=\frac{28}{3}$
$x=9\frac{1}{3}$
Hence, third proportional is $9\frac{1}{3}$