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Let the length be (x+0.75) and the width be x:

length*width = area

(x+0.75)*x = 11.25 square inches

x2+0.75x = 11.25

x2+0.75x-11.25 = 0

Solving the above equation by means of the quadratic equation formula gives a positive value of 3 for x.

Therefore: length = 3.75 inches and width = 3 inches

Check: 3.75*3 = 11.25 square inches

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Q: What are the dimensions of a rectangle whose length is 0.75 inches longer than its width and has an area of 11.25 square inches?
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