MathDB

17

Part of 1985 AMC 12/AHSME

Problems(1)

Finding the Area of a Rectangle

Source:

3/3/2009
Diagonal DB DB of rectangle ABCD ABCD is divided into 3 3 segments of length 1 1 by parallel lines L L and L′ L' that pass through A A and C C and are perpendicular to DB DB. The area of ABCD ABCD, 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("LL", (x/2,0), SW); label("L′L^\prime", C, SW);
label("1", D--F, NW); label("1", F--E, SE); label("1", E--B, SE); clip(W--X--Y--Z--cycle); [/asy]
<spanclass=′latex−bold′>(A)</span> 4.1<spanclass=′latex−bold′>(B)</span> 4.2<spanclass=′latex−bold′>(C)</span> 4.3<spanclass=′latex−bold′>(D)</span> 4.4<spanclass=′latex−bold′>(E)</span> 4.5 <span class='latex-bold'>(A)</span>\ 4.1 \qquad <span class='latex-bold'>(B)</span>\ 4.2 \qquad <span class='latex-bold'>(C)</span>\ 4.3 \qquad <span class='latex-bold'>(D)</span>\ 4.4 \qquad <span class='latex-bold'>(E)</span>\ 4.5
geometryrectangleratio