Diesel Inc. is making rectangular picture frames for a new product being launched at the end of the year. To keep the weight down, the area of the frame should be 18 cm2. The inside of the frame has to be 11 cm by 6 cm. What should the width of the frame be?
Let w be the width of the frame.
The length of the shorter strip of frame is 6 + 2w cm
The length of the longer strip (excluding that on the shorter sides) is 11 cm
The total area of the frame is then given by 2*(6+2w)*w + 2*11*w or 4w2 + 34w cm
This must equal 18 cm2, so:
4w2 +34w = 18
Divide by 2 and rearrange: 2w2 + 17w - 9 = 0
This factors as: (2w - 1)(w + 9) = 0
Because the width must be positive the only sensible solution of this is 2w = 1, or w = 1/2 cm