2011 AMC 10A Problems/Problem 9

Problem 9

A rectangular region is bounded by the graphs of the equations $y=a, y=-b, x=-c,$ and $x=d$ , where $a,b,c,$ and $d$ are all positive numbers. Which of the following represents the area of this region?

$\textbf{(A)}\ ac+ad+bc+bd\qquad\textbf{(B)}\ ac-ad+bc-bd\qquad\textbf{(C)}\ ac+ad-bc-bd \quad\quad\qquad\textbf{(D)}\ -ac-ad+bc+bd\qquad\textbf{(E)}\ ac-ad-bc+bd$

Solution

We have a rectangle of side lengths $a-(-b)=a+b$ and $d-(-c)=c+d.$ Thus the area of this rectangle is \[ (a + b)(c + d) = ac + ad + bc + bd. \]

2011 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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2011 AMC 10A Problems/Problem 9

Problem 9

Solution

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