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MATH / Squares are constructed on each of the sides of triangle △ABC, as shown. If the perimeter of △ABC is 17, then what is the perimeter of the nine-sided figure that is composed of the…

Problem

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

problem

Squares are constructed on each of the sides of triangle △ABC\triangle ABC, as shown. If the perimeter of △ABC\triangle ABC is 17, then what is the perimeter of the nine-sided figure that is composed of the remaining three sides of each of the squares? [asy] import olympiad; size(150); defaultpen(linewidth(0.8)); dotfactor=4; picture a; draw(a,(0,0)--(3,0)--(0,4)--cycle); label("AA",(-2.1,-2.2),SW); label("BB",(3.1,-2.2),SE); label("CC",(0.05,0.3),N); draw(a,(3,0)--(3,-3)--(0,-3)--(0,0)); draw(a,(0,0)--(-4,0)--(-4,4)--(0,4)); draw(a,shift(-2.4,2.2)*rotate(90 - aTan(4/3))*((3,0)--(8,0)--(8,-5)--(3,-5))); add(currentpicture,rotate(-130)*a); [/asy]
Plain-text mathematical notation (without MathML)
Squares are constructed on each of the sides of triangle △ABC, as shown.  If the perimeter of △ABC is 17, then what is the perimeter of the nine-sided figure that is composed of the remaining three sides of each of the squares? [asy]
import olympiad; size(150); defaultpen(linewidth(0.8)); dotfactor=4;
picture a;
draw(a,(0,0)--(3,0)--(0,4)--cycle);
label("A",(-2.1,-2.2),SW);
label("B",(3.1,-2.2),SE);
label("C",(0.05,0.3),N);
draw(a,(3,0)--(3,-3)--(0,-3)--(0,0));
draw(a,(0,0)--(-4,0)--(-4,4)--(0,4));
draw(a,shift(-2.4,2.2)*rotate(90 - aTan(4/3))*((3,0)--(8,0)--(8,-5)--(3,-5)));
add(currentpicture,rotate(-130)*a);
[/asy]
Original LaTeX notation
Squares are constructed on each of the sides of triangle $\triangle ABC$, as shown.  If the perimeter of $\triangle ABC$ is 17, then what is the perimeter of the nine-sided figure that is composed of the remaining three sides of each of the squares? [asy]
import olympiad; size(150); defaultpen(linewidth(0.8)); dotfactor=4;
picture a;
draw(a,(0,0)--(3,0)--(0,4)--cycle);
label("$A$",(-2.1,-2.2),SW);
label("$B$",(3.1,-2.2),SE);
label("$C$",(0.05,0.3),N);
draw(a,(3,0)--(3,-3)--(0,-3)--(0,0));
draw(a,(0,0)--(-4,0)--(-4,4)--(0,4));
draw(a,shift(-2.4,2.2)*rotate(90 - aTan(4/3))*((3,0)--(8,0)--(8,-5)--(3,-5)));
add(currentpicture,rotate(-130)*a);
[/asy]

level

Level 4

type

Prealgebra

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Source and history

task_id
5d839e60-da5d-5234-af53-6307ca147c74
task_key
prealgebra--test--5d839e60-da5d-5234-af53-6307ca147c74
task_revision_id
1
config / split
prealgebra / test

Official source

initial import