Question

Form all possible proportions of the numbers $8,27,9and24$

Answer 1

Now, we know that for four numbers $a,b,candd$

If $a:b::c:d$be in proportion then

$a\times d=b\times c$ -------------------------------- $eq\left(1\right)$

So we have to find all possible arrangements

Now in $8,27,9and24$

$8\times 27=9\times 24$

Then by $eq\left(1\right)$ we have first proportion be

$8:9::24:27$

Again,

$24\times 9=8\times 27$

Then by $eq\left(1\right)$ we have Second proportion

$24:8::27:9$

Again,

$8\times 27=24\times 9$

Then by $eq\left(1\right)$ we have third proportion

$8:24::9:27$

Again,

$9\times 24=8\times 27$

Then by $eq\left(1\right)$ we have fourth proportion

$9:8::27:24$

Hence all possible proportion is

$8:9:24:27$, $24:8:27:9$, $8:24::9:27$ & $9:8::27:24$.