![]() For instance, 6 times 4 is 24, whereas 7 times 3 is 21. Meaning, we can actually make a claim on the product of numbers: As the numbers come closer together, their product will increase. The reason being, the square will always have more area as the difference of squares is being applied. Hence, there is a direct correlation to our area comparison and the grade 10 math logic. Sure, but how does this help us? To best the connection of the difference of squares to the comparison of the square and the rectangle, let’s convert the dimensions of our rectangle: Now, if we remember back to our grade 10 unit regarding quadratic equations, you will remember a special binomial called the ‘Difference of squares’. When we look at the 7 by 3 rectangle, what we actually realize is that the dimensions are formed by either adding or subtracting 2 from the side length (of the square) 5. In addition, let’s see how we can use this additional knowledge to solve other problems very quickly. ![]() ![]() Thus, let’s understand what’s happening behind the scenes. However, this is not the case: The rectangle’s area is smaller than that of the square. Although we are told that squares have more area than rectangles (where the average of the length and width is equal to the side length of the square), why does this actually occur? More importantly, one would assume that the area should stay the same as you are increasing and decreasing the length of the square to form the new dimensions of the rectangle.
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