Difference between revisions of "2011 AMC 8 Problems/Problem 13"
(Created page with "The overlap length is 5, so the shaded area is 5 * 15 =75. The area of the whole shape is 25*15 = 375 The fraction 75/375 reduces to 1/5 or 20%.") |
(Typed the problem, but still needs a solution) |
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− | + | 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? | |
− | + | <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> | ||
+ | |||
+ | <math> \textbf{(A)}\ 15\qquad\textbf{(B)}\ 18\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 24\qquad\textbf{(E)}\ 25 </math> |
Revision as of 18:45, 4 November 2012
Two congruent squares, and
, have side length
. They overlap to form the
by
rectangle
shown. What percent of the area of rectangle
is shaded?