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MATH / Each triangle in this figure is an isosceles right triangle. The length of…

Problem

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

problem

Each triangle in this figure is an isosceles right triangle. The length of BC¯\overline{BC} is 2 units. What is the number of units in the perimeter of quadrilateral ABCDABCD? Express your answer in simplest radical form. [asy] draw((0,0)--(10,0)--(0,10)--cycle); draw((10,0)--(0,10)--(10,20)--cycle); draw((1,0)--(1,1)--(0,1)); draw((1,11)--(2,10)--(1,9)); label("AA",(0,0),S); label("BB",(10,0),S); label("CC",(10,20),N); label("DD",(0,10),W); [/asy]
Plain-text mathematical notation (without MathML)
Each triangle in this figure is an isosceles right triangle. The length of (BC)¯ is 2 units. What is the number of units in the perimeter of quadrilateral ABCD? Express your answer in simplest radical form.

[asy]
draw((0,0)--(10,0)--(0,10)--cycle);
draw((10,0)--(0,10)--(10,20)--cycle);
draw((1,0)--(1,1)--(0,1));
draw((1,11)--(2,10)--(1,9));
label("A",(0,0),S);
label("B",(10,0),S);
label("C",(10,20),N);
label("D",(0,10),W);

[/asy]
Original LaTeX notation
Each triangle in this figure is an isosceles right triangle. The length of $\overline{BC}$ is 2 units. What is the number of units in the perimeter of quadrilateral $ABCD$? Express your answer in simplest radical form.

[asy]
draw((0,0)--(10,0)--(0,10)--cycle);
draw((10,0)--(0,10)--(10,20)--cycle);
draw((1,0)--(1,1)--(0,1));
draw((1,11)--(2,10)--(1,9));
label("$A$",(0,0),S);
label("$B$",(10,0),S);
label("$C$",(10,20),N);
label("$D$",(0,10),W);

[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
f580a9b8-7912-57c5-8997-9f259d12410b
task_key
geometry--test--f580a9b8-7912-57c5-8997-9f259d12410b
task_revision_id
1
config / split
geometry / test

Official source

initial import