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
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.
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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