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MATH / Square ABCD has side length 10. Point E is on (BC)¯, and the area of △ABE is 40. What is BE? [asy]size(4cm); pair A,B,C,D,E; A=(0,0); B=(0,50); C=(50,50); D=(50,0); E = (30,50); dr…

Problem

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

problem

Square ABCD ABCD has side length 1010. Point EE is on BC¯\overline{BC}, and the area of △ABE \triangle ABE is 4040. What is BE BE ? [asy]size(4cm); pair A,B,C,D,E; A=(0,0); B=(0,50); C=(50,50); D=(50,0); E = (30,50); draw(A--B); draw(B--E); draw(E--C); draw(C--D); draw(D--A); draw(A--E); dot(A); dot(B); dot(C); dot(D); dot(E); label("AA",A,SW); label("BB",B,NW); label("CC",C,NE); label("DD",D,SE); label("EE",E,N); [/asy]
Plain-text mathematical notation (without MathML)
Square ABCD has side length 10. Point E is on (BC)¯, and the area of △ABE is 40. What is BE? [asy]size(4cm);
pair A,B,C,D,E;
A=(0,0);
B=(0,50);
C=(50,50);
D=(50,0);
E = (30,50);
draw(A--B);
draw(B--E);
draw(E--C);
draw(C--D);
draw(D--A);
draw(A--E);
dot(A);
dot(B);
dot(C);
dot(D);
dot(E);
label("A",A,SW);
label("B",B,NW);
label("C",C,NE);
label("D",D,SE);
label("E",E,N);
[/asy]
Original LaTeX notation
Square $ ABCD $ has side length $10$. Point $E$ is on $\overline{BC}$, and the area of $ \triangle ABE $ is $40$. What is $ BE $? [asy]size(4cm);
pair A,B,C,D,E;
A=(0,0);
B=(0,50);
C=(50,50);
D=(50,0);
E = (30,50);
draw(A--B);
draw(B--E);
draw(E--C);
draw(C--D);
draw(D--A);
draw(A--E);
dot(A);
dot(B);
dot(C);
dot(D);
dot(E);
label("$A$",A,SW);
label("$B$",B,NW);
label("$C$",C,NE);
label("$D$",D,SE);
label("$E$",E,N);
[/asy]

level

Level 1

type

Geometry

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Source and history

task_id
f6f3e025-125c-5d1c-a530-7f319414e96e
task_key
geometry--test--f6f3e025-125c-5d1c-a530-7f319414e96e
task_revision_id
1
config / split
geometry / test

Official source

initial import