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MATH / In the figure below, quadrilateral CDEG is a square with CD=3, and quadrilateral BEFH is a rectangle. If BE=5, how many units is BH? Express your answer as a mixed number. [asy] un…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In the figure below, quadrilateral CDEGCDEG is a square with CD=3CD = 3, and quadrilateral BEFHBEFH is a rectangle. If BE=5BE = 5, how many units is BHBH? Express your answer as a mixed number. [asy] unitsize(5mm); defaultpen(linewidth(.7pt)+fontsize(8pt)); pair A=(0,0), B=(3,0), C=(6,0), D=(9,0), Ep=(9,3), G=(6,3); pair F0=bisectorpoint(B,2*Ep-B), H0=bisectorpoint(Ep,2*B-Ep); pair H=extension(B,H0,A,G); pair F=extension(Ep,F0,A,G); draw(H--B--Ep--F--A--D--Ep--G--C); label("AA",A,S); label("BB",B,S); label("CC",C,S); label("DD",D,S); label("EE",Ep,E); label("FF",F,N); label("GG",G,NW); label("HH",H,NW); [/asy]
Plain-text mathematical notation (without MathML)
In the figure below, quadrilateral CDEG is a square with CD=3, and quadrilateral BEFH is a rectangle. If BE=5, how many units is BH? Express your answer as a mixed number. [asy]
unitsize(5mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));

pair A=(0,0), B=(3,0), C=(6,0), D=(9,0), Ep=(9,3), G=(6,3);
pair F0=bisectorpoint(B,2*Ep-B), H0=bisectorpoint(Ep,2*B-Ep);
pair H=extension(B,H0,A,G);
pair F=extension(Ep,F0,A,G);

draw(H--B--Ep--F--A--D--Ep--G--C);
label("A",A,S);
label("B",B,S);
label("C",C,S);
label("D",D,S);
label("E",Ep,E);
label("F",F,N);
label("G",G,NW);
label("H",H,NW);
[/asy]
Original LaTeX notation
In the figure below, quadrilateral $CDEG$ is a square with $CD = 3$, and quadrilateral $BEFH$ is a rectangle. If $BE = 5$, how many units is $BH$? Express your answer as a mixed number. [asy]
unitsize(5mm);
defaultpen(linewidth(.7pt)+fontsize(8pt));

pair A=(0,0), B=(3,0), C=(6,0), D=(9,0), Ep=(9,3), G=(6,3);
pair F0=bisectorpoint(B,2*Ep-B), H0=bisectorpoint(Ep,2*B-Ep);
pair H=extension(B,H0,A,G);
pair F=extension(Ep,F0,A,G);

draw(H--B--Ep--F--A--D--Ep--G--C);
label("$A$",A,S);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,S);
label("$E$",Ep,E);
label("$F$",F,N);
label("$G$",G,NW);
label("$H$",H,NW);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
c3e5af3c-1d7a-5707-bdf4-d843de289637
task_key
geometry--test--c3e5af3c-1d7a-5707-bdf4-d843de289637
task_revision_id
1
config / split
geometry / test

Official source

initial import