Real World Math Problem!

[NickPDanger]

I'm a graphic designer at a sign company, and we work with area often. Occasionally the client will say, "The sign looks good, but I need you to scale it down to "x" square feet to comply with city regulations. City regulations let me measure area by a "rectilinear shape with no more than 8 sides".
This leaves me with a frequently encountered real-world problem that I would love for you guys to have a crack at. What I'm looking for is a formula that I can use whenever we run into this. This is kind of a word/visual problem, but I suspect it will have mostly algebra. Take a look at this image.

http://postimg.org/image/46cjqxnrl/

The purple area is 26 square inches with overall dimensions of 5x10 inches. What is the simplest formula for scaling the overall dimensions to achieve a purple area that is 22 square inches?

Thanks!
Nick

 

[stapel]

...This is kind of a word/visual problem, but I suspect it will have mostly algebra. Take a look at this image.

http://postimg.org/image/46cjqxnrl/

The purple area is 26 square inches with overall dimensions of 5x10 inches. What is the simplest formula for scaling the overall dimensions to achieve a purple area that is 22 square inches?

What is the current area? What is the target area? Set up a percentage equation for the situation (go here to refresh on how to do that):

. . . . .(target area) is (some percentage) of (original area)

Solve for the percentage. This tells you the percentage that the target area is of the original area. Then recall how the linear scale factor relates to the area (that is, to the squared) scale factor. Use this information to make the appropriate adjustments to the linear dimensions.

If you get stuck, please reply showing your work so far. Thank you!