• Dec 21st 2007, 08:15 AM
jenko
hi i also have this other equation which i am unsure of, just wondering if you can help which is:

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.

thanks again!
jenko!
• Dec 21st 2007, 08:58 AM
Soroban
Hello, jenko!

Did you make a sketch?

Quote:

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: . $x$ mm.
. . Its area is: . $x^2$ mm².

The side of the hole is: . $x - 40$ mm.
. . Its area is: . $(x-40)^2$ m².

The area of the hole is one-third the area of the plate.
. . There is our equation! . . . . . $(x-40)^2 \:=\:\frac{1}{3}x^2$