Difference between revisions of "2011 AMC 8 Problems/Problem 13"

Revision as of 17:45, 4 November 2012

Two congruent squares, $ABCD$ and $PQRS$ , have side length $15$ . They overlap to form the $15$ by $25$ rectangle $AQRD$ shown. What percent of the area of rectangle $AQRD$ is shaded? $[asy] filldraw((0,0)--(25,0)--(25,15)--(0,15)--cycle,white,black); label("D",(0,0),S); label("R",(25,0),S); label("Q",(25,15),N); label("A",(0,15),N); filldraw((10,0)--(15,0)--(15,15)--(10,15)--cycle,mediumgrey,black); label("S",(10,0),S); label("C",(15,0),S); label("B",(15,15),N); label("P",(10,15),N);[/asy]$

$\textbf{(A)}\ 15\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 24\qquad\textbf{(E)}\ 25$

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Difference between revisions of "2011 AMC 8 Problems/Problem 13"

Revision as of 17:45, 4 November 2012

@@ Line 1: / Line 1: @@
-The overlap length is 5, so the shaded area is 5 * 15 =75.
+Two congruent squares, <math>ABCD</math> and <math>PQRS</math>, have side length <math>15</math>. They overlap to form the <math>15</math> by <math>25</math> rectangle <math>AQRD</math> shown. What percent of the area of rectangle <math>AQRD</math> is shaded?
-The area of the whole shape is 25*15 = 375
+<asy>
-The fraction 75/375 reduces to 1/5 or 20%.
+filldraw((0,0)--(25,0)--(25,15)--(0,15)--cycle,white,black);
+label("D",(0,0),S);
+label("R",(25,0),S);
+label("Q",(25,15),N);
+label("A",(0,15),N);
+filldraw((10,0)--(15,0)--(15,15)--(10,15)--cycle,mediumgrey,black);
+label("S",(10,0),S);
+label("C",(15,0),S);
+label("B",(15,15),N);
+label("P",(10,15),N);</asy>
+<math> \textbf{(A)}\ 15\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 24\qquad\textbf{(E)}\ 25 </math>