2005 AMC 10A Problems/Problem 8: Difference between revisions
Created page with '== Problem 8 == In the figure, the length of side <math>AB</math> of square <math>ABCD</math> is <math>\sqrt{50}</math> and <math>BE</math>=1. What is the area of the inner squar…' |
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== Problem | == Problem == | ||
In the figure, the length of side <math>AB</math> of square <math>ABCD</math> is <math>\sqrt{50}</math> and <math>BE</math>=1. What is the area of the inner square <math>EFGH</math>? | In the figure, the length of side <math>AB</math> of square <math>ABCD</math> is <math>\sqrt{50}</math> and <math>BE</math>=1. What is the area of the inner square <math>EFGH</math>? | ||
[asy] | |||
pair D = (0,0); pair C = (1,0); pair B = (1,1); pair A = (0,1); pair H = (0.25,0.6); pair E = foot(C,H,B); pair F = foot(D,C,E); pair G = foot(A,D,F); pair H2 = foot(B,A,G); draw(A--B--C--D--cycle,linewidth(1)); draw(B--H2,linewidth(1)); draw(C--E,linewidth(1)); draw(D--F,linewidth(1)); draw(A--G,linewidth(1)); label("<math>A</math>",A,NW);label("<math>B</math>",B,NE);label("<math>C</math>",C,SE);label("<math>D</math>",D,SW); label("<math>H</math>",H2,SW);label("<math>G</math>",G,SE);label("<math>F</math>",F,NE);label("<math>E</math>",E,NW);[/asy] | |||
<math> \textbf{(A)}\ 25\qquad\textbf{(B)}\ 32\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 40\qquad\textbf{(E)}\ 42 </math> | |||
Revision as of 14:36, 24 December 2009
Problem
In the figure, the length of side 
of square 
is 
and 
=1. What is the area of the inner square 
?
[asy]
pair D = (0,0); pair C = (1,0); pair B = (1,1); pair A = (0,1); pair H = (0.25,0.6); pair E = foot(C,H,B); pair F = foot(D,C,E); pair G = foot(A,D,F); pair H2 = foot(B,A,G); draw(A--B--C--D--cycle,linewidth(1)); draw(B--H2,linewidth(1)); draw(C--E,linewidth(1)); draw(D--F,linewidth(1)); draw(A--G,linewidth(1)); label("
",A,NW);label("
",B,NE);label("
",C,SE);label("
",D,SW); label("
",H2,SW);label("
",G,SE);label("
",F,NE);label("
",E,NW);[/asy]
