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MATH / Triangle ABC and triangle DEF are congruent, isosceles right triangles. The square inscribed in triangle ABC has an area of 15 square centimeters. What is the area of the square in…

Problem

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

problem

Triangle ABCABC and triangle DEFDEF are congruent, isosceles right triangles. The square inscribed in triangle ABCABC has an area of 15 square centimeters. What is the area of the square inscribed in triangle DEFDEF? Express your answer as a common fraction. [asy] draw((0,0)--(2,0)--(0,2)--(0,0)--cycle,linewidth(2)); draw((0,0)--(1,0)--(1,1)--(0,1)--(0,0)--cycle,linewidth(2)); draw((1/8,0)--(1/8,1/8)--(0,1/8),linewidth(1)); draw((3,0)--(5,0)--(3,2)--(3,0)--cycle,linewidth(2)); draw((3+2/3,0)--(3+4/3,2/3)--(3+2/3,4/3)--(3,2/3)--(3+2/3,0)--cycle,linewidth(2)); draw((3+1/8,0)--(3+1/8,1/8)--(3,1/8),linewidth(1)); label("A",(0,2),NW); label("B",(0,0),SW); label("C",(2,0),SE); label("D",(3,2),NW); label("E",(3,0),SW); label("F",(5,0),SE); [/asy]
Plain-text mathematical notation (without MathML)
Triangle ABC and triangle DEF are congruent, isosceles right triangles. The square inscribed in triangle ABC has an area of 15 square centimeters. What is the area of the square inscribed in triangle DEF? Express your answer as a common fraction.

[asy]
draw((0,0)--(2,0)--(0,2)--(0,0)--cycle,linewidth(2));
draw((0,0)--(1,0)--(1,1)--(0,1)--(0,0)--cycle,linewidth(2));
draw((1/8,0)--(1/8,1/8)--(0,1/8),linewidth(1));

draw((3,0)--(5,0)--(3,2)--(3,0)--cycle,linewidth(2));
draw((3+2/3,0)--(3+4/3,2/3)--(3+2/3,4/3)--(3,2/3)--(3+2/3,0)--cycle,linewidth(2));
draw((3+1/8,0)--(3+1/8,1/8)--(3,1/8),linewidth(1));

label("A",(0,2),NW);
label("B",(0,0),SW);
label("C",(2,0),SE);

label("D",(3,2),NW);
label("E",(3,0),SW);
label("F",(5,0),SE);

[/asy]
Original LaTeX notation
Triangle $ABC$ and triangle $DEF$ are congruent, isosceles right triangles. The square inscribed in triangle $ABC$ has an area of 15 square centimeters. What is the area of the square inscribed in triangle $DEF$? Express your answer as a common fraction.

[asy]
draw((0,0)--(2,0)--(0,2)--(0,0)--cycle,linewidth(2));
draw((0,0)--(1,0)--(1,1)--(0,1)--(0,0)--cycle,linewidth(2));
draw((1/8,0)--(1/8,1/8)--(0,1/8),linewidth(1));

draw((3,0)--(5,0)--(3,2)--(3,0)--cycle,linewidth(2));
draw((3+2/3,0)--(3+4/3,2/3)--(3+2/3,4/3)--(3,2/3)--(3+2/3,0)--cycle,linewidth(2));
draw((3+1/8,0)--(3+1/8,1/8)--(3,1/8),linewidth(1));

label("A",(0,2),NW);
label("B",(0,0),SW);
label("C",(2,0),SE);

label("D",(3,2),NW);
label("E",(3,0),SW);
label("F",(5,0),SE);

[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
3f32cf2e-ed2b-56a6-bf53-62d07db1be4c
task_key
geometry--test--3f32cf2e-ed2b-56a6-bf53-62d07db1be4c
task_revision_id
1
config / split
geometry / test

Official source

initial import