```Question 325398
<pre><b>

{{{drawing(400,400,-1,16,-1,16, green(rectangle(0,0,7,7)), locate(3.4,0,x), locate(-.5,3.6,x),locate(7.3,3.5,x),locate(3.4,7.6,x)  )}}}

Now let's add 8 cm to each side:

{{{drawing(400,400,-1,16,-1,16, green(rectangle(0,0,7,7)), locate(3.4,0,x), locate(-.5,3.6,x),locate(7.3,3.5,x),locate(3.4,7.6,x),
red(triangle(7,0,15,0,8,0),triangle(15,0,15,15,15,0),triangle(0,15,15,15,0,15),triangle(0,15,0,7,0,7)), locate(-.5,11,8), locate(11,0,8)

)}}}

Now each side of the big square has length of side x plus the 8cm

So each side of the big square is x+8 cm.

Now we use the formula for the area of a square:

{{{Area}}}{{{""=""}}}{{{(one_side)^2}}}

We are told

>>...area becomes 225cm<sup>2</sup>...<<

So we substitute 225 for A and (x+8) for "one side"

{{{225}}}{{{""=""}}}{{{(x+8)^2}}}

{{{(x+8)^2}}}{{{""=""}}}{{{225}}}

Take square roots of both side:

{{{sqrt((x+8)^2)}}}{{{""=""}}}{{{sqrt(225)}}}

{{{x+8}}}{{{""=""}}}{{{15}}}

{{{x}}}{{{""=""}}}{{{7}}}

So each side of the original square had length 7 cm.

Edwin</pre> ```