Your company is making frames for a 5”x7” picture. If the area of the frame needs to be 64 square inches, how wide must the frame be?

Question

I'm just having problems with this math problem and would like some help please

Answer 1

Hi Ash,

As a former picture framer, I encountered this type of problem many times. It is important to remember that the width of the frame border  must be doubled when adding it to the picture dimensions since the frame is on both sides of the picture!

So if w is the width of the frame border, then the equation becomes

(5+2w)(7+2w) = 64.

Use the quadratic formula to solve this and the answer for w is 1.03in.

I hope this helps.

Answer 2

8" x 8" would work, since both dimensions are bigger than the picture's dimensions. Let's assume your company wants to make frames with a constant border, though.

 

Let x = border width (in inches).

 

Then (5 + x)*(7 + x) = 64. Solve for x. This isn't factorable, so use the quadratic formula.

 

It should work out to somewhere just over 2 inches, since a 7" x 9" frame (2 inch border) is 63 square inches.

 

The frame then needs to be just over 7" wide, or just over 9" wide, depending on what's in the photo.