Expert: Scott A Wilson - 11/18/2010

Question
A square photo graph of unknown dimensions  (X by X) is to be place on a rectangular background that is 6 inches longer than the photo and 3 inches wider than the photo.  

You must first determine how to now represent the length and width of the rectangular background.

If the area of the rectangular background is to be 340 sq. inches write an equation using   A = l x w and solve the equation and tell the dimensions  (X by X) of the original photograph.

accurately determine an equation using   A = l x w and solve the equation then, tell the dimensions  (X by X) of the original photograph.  

Answer
The picture is X by X.
The background is 6 inches higher and 3 inches higher,
so the area is (X+6)(X+3) = x^2 + 9X + 18.

If the area is 340, then x^2 + 9X + 18 = 340 .
Subtracting 340 from both sides gives x^2 + 9x - 322 = 0.

Now 322 = 2*161, and 161 = 7*23, so  322 = 14*23.
Note that 23 - 14 = 9, so it factors into (x+23)(x-9).

That says x+23 = 0 or x-9 = 0.  This makes x = -23 or x = 9.
In order for that to make sense, only one x value can be chosen.