Hello, jenko!

Did you make a sketch?

A square steel plate is pierced by a square tool leaving a margin of 20mm all round.

The area of the hole is one-third of that of the original plate.

Calculate the dimensions of the original plate. Code:

: 20 : x-40 : 20 :
- * - - - - - - - - - - - * -
20 | | :
- | * - - - - - * | :
: | | | | :
: | | | | :
x-40 | | x-40 | | x
: | | | | :
: | | x-40 | | :
- | * - - - - - * | :
20 | | :
- * - - - - - - - - - - - * -
: - - - - - x - - - - - :

The side of the original plate is: .$\displaystyle x$ mm.

. . Its area is: .$\displaystyle x^2$ mm².

The side of the hole is: .$\displaystyle x - 40$ mm.

. . Its area is: .$\displaystyle (x-40)^2$ m².

The area of the hole is one-third the area of the plate.

. . There is our equation! . . . . . $\displaystyle (x-40)^2 \:=\:\frac{1}{3}x^2$