Question 807750
Let {{{x}}} be the length of one side of {{{square}}} pan.

Then,the area of the square pan is {{{x^2}}}.

If the other pan's one side is {{{6cm}}} narrower and other side {{{8cm}}} longer, than other pan's area is:

{{{(x-6)(x+8)}}}

Since given that both areas are same, we now have:

{{{x^2 = (x-6)(x+8)}}}

FOIL the right:

{{{x^2 = x^2+8x-6x-48}}}

{{{0 = 8x-6x-48}}}

{{{0 = 2x-48}}}

{{{48 = 2x}}}

{{{x=24cm }}}

So, the square pan is {{{24cm}}} by {{{24cm}}} and area is {{{24cm*24cm=576cm^2}}}

The other pan is:

{{{(x-6)}}} by {{{(x+8)}}}

{{{(24-6)}}} by {{{(24+8)}}}

{{{18cm}}} by {{{32cm}}} (size of other pan)

and the area is {{{18cm*32cm=576cm^2}}}