SOLUTION: Please help me solve this equation: the area of a frame is equal to the area of 4"x6" photo it surrounds. the frame is of uniform width. how wide is the frame?

Question 130599This question is from textbook
: Please help me solve this equation: the area of a frame is equal to the area of 4"x6" photo it surrounds. the frame is of uniform width. how wide is the frame? This question is from textbook

Found 2 solutions by ilana, solver91311:
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
The frame is a rectangle with a rectangle cut out of it. The area of the frame is 4*6=24 square inches. So the area of the big rectangle (frame and picture) is 48 square inches. (Draw a picture and it will help.) Let's call the width of the frame x. So the distance from the edge of the picture to the edge of the frame is x at any edge. So the equation is (6+2x)(4+2x)=48. Expand this and solve for x and you get x=-6,1. x is a distance, so it must be 1. So the frame is 1 inch wide.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The outside dimensions of the frame, as we can see from the picture are and , so the area of the overall thing, frame and the picture inside must be , so the area covered by the frame only must be , because we have to subtract the area of the picture. It is also given that this area must be equal to the picture it surrounds, , so we can write:

Apply FOIL and put everything on the left:

Collect terms:

Divide by 4:

Use the quadratic formula because there are no rational factors:

But so exclude this root -- we are looking for a positive number measure of length.

Therefore the width of the frame (x in the figure) is exactly inches or approximately 1.16 inches.
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