SOLUTION: Placing a photograph behind a 12-inch by 12 inch piece of matting. The photograph is to be positioned so that the matting is twice as wide at the top and bottom as it is at the si

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Placing a photograph behind a 12-inch by 12 inch piece of matting. The photograph is to be positioned so that the matting is twice as wide at the top and bottom as it is at the si      Log On


   

Question 28141: Placing a photograph behind a 12-inch by 12 inch piece of matting. The photograph is to be positioned so that the matting is twice as wide at the top and bottom as it is at the sides. If the area of the photograph is to be 54 square inches, what are the dimensions? I do not understand how to set this up into a quadratic equation.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
first, draw the diagram.

Draw a square... 12 by 12 depicting the matting and then draw a rectangle inside, representing the picture.

Let the width between the picture and the matting be x
Let the height between the picture and the matting be 2x

So, width of picture is (12-2x)
and height of picture is (12-4x)

area of picture is (12-2x)(12-4x) = 54

Multiply it out, collect terms, make it equal to zero and then factorise.

Answers are x=7.5 or 1.5
only 1.5 makes sense.... this gives dimensions of 9 by 6.

jon.