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I'm confused about this question... Please Help!

 Jun 2, 2018
 #1
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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

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