Finding the Area of a Rectangle
Source:
March 3, 2009
geometryrectangleratio
Problem Statement
Diagonal of rectangle is divided into segments of length by parallel lines and that pass through and and are perpendicular to . The area of , rounded to the nearest tenth, is[asy]size(200);
defaultpen(linewidth(0.7)+fontsize(10));
real x=sqrt(6), y=sqrt(3), a=0.4;
pair D=origin, A=(0,y), B=(x,y), C=(x,0), E=foot(C,B,D), F=foot(A,B,D);
real r=degrees(B);
pair M1=F+3*dir(r)*dir(90), M2=F+3*dir(r)*dir(-90), N1=E+3*dir(r)*dir(90), N2=E+3*dir(r)*dir(-90);
markscalefactor=0.02;
draw(B--C--D--A--B--D^^M1--M2^^N1--N2^^rightanglemark(A,F,B,6)^^rightanglemark(N1,E,B,6));
pair W=A+a*dir(135), X=B+a*dir(45), Y=C+a*dir(-45), Z=D+a*dir(-135);label("A", A, NE);
label("B", B, NE);
label("C", C, dir(0));
label("D", D, dir(180));
label("", (x/2,0), SW);
label("", C, SW);label("1", D--F, NW);
label("1", F--E, SE);
label("1", E--B, SE);
clip(W--X--Y--Z--cycle);
[/asy]