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# ​Given that a > b, which of the shaded regions is larger. Justify your reasoning.

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Jun 2, 2018

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We meet again, Rick!

The shaded region, I would presume anyway, also happens to be the area of a rectangle. Let's take a guess and say that the left figure has more area. To confirm (or disprove) this, one must find the areas of the rectangles.

 $$\text{left }\boxed{\quad}=a(b+2)$$ $$\text{right}\boxed{\quad}=b(a+2)$$ Let's assume that the left rectangle has more area and see what happens. $$a(b+2) < b(a+2)$$ Now, solve. This will allow you to figure out the relationship between a and b. Distribute. $$ab+2a < ab+2b$$ The ab's cancel out. $$2a<2b$$ Divide by 2 on both sides. $$a < b$$

What is this result telling you or me? It tells you that, in order for the leftward rectangle to have more area, a must be less than b. Of course, this cannot be; the original problem states that $$a>b$$ . We have reached a contradiction. Therefore, the rightward rectangle has more area!

Jun 3, 2018
edited by TheXSquaredFactor  Jun 3, 2018