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MATH / A greeting card is 6 inches wide and 8 inches tall. Point A is 3 inches from the…

Problem

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

problem

A greeting card is 6 inches wide and 8 inches tall. Point A is 3 inches from the fold, as shown. As the card is opened to an angle of 45 degrees, through how many more inches than point A does point B travel? Express your answer as a common fraction in terms of π\pi. [asy] import olympiad; import geometry; size(150); defaultpen(linewidth(0.8)); draw((0,0)--(6,0)--(6,8)--(0,8)--cycle); filldraw((0,0)--(5,-1)--(5,7)--(0,8)--cycle,fillpen=white); pair A = 0.5*((0,8)+(5,7)); label("AA",A,SW); dot((5,7)); dot(A); label("BB",(5,7),SW); label("$8''$",(0,0)--(0,8),W);label("$6''$",(0,0)--(5,-1),S); point C = (2.5,3.5); label(rotate(-aTan(1/5))*scale(0.8)*"Happy Birthday!",C); [/asy]
Plain-text mathematical notation (without MathML)
A greeting card is 6 inches wide and 8 inches tall. Point A is 3 inches from the fold, as shown. As the card is opened to an angle of 45 degrees, through how many more inches than point A does point B travel? Express your answer as a common fraction in terms of π. [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
draw((0,0)--(6,0)--(6,8)--(0,8)--cycle);
filldraw((0,0)--(5,-1)--(5,7)--(0,8)--cycle,fillpen=white);

pair A = 0.5*((0,8)+(5,7));
label("A",A,SW);
dot((5,7));
dot(A); label("B",(5,7),SW);
label("$8''$",(0,0)--(0,8),W);label("$6''$",(0,0)--(5,-1),S);
point C = (2.5,3.5);
label(rotate(-aTan(1/5))*scale(0.8)*"Happy Birthday!",C);
[/asy]
Original LaTeX notation
A greeting card is 6 inches wide and 8 inches tall. Point A is 3 inches from the fold, as shown. As the card is opened to an angle of 45 degrees, through how many more inches than point A does point B travel? Express your answer as a common fraction in terms of $\pi$. [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
draw((0,0)--(6,0)--(6,8)--(0,8)--cycle);
filldraw((0,0)--(5,-1)--(5,7)--(0,8)--cycle,fillpen=white);

pair A = 0.5*((0,8)+(5,7));
label("$A$",A,SW);
dot((5,7));
dot(A); label("$B$",(5,7),SW);
label("$8''$",(0,0)--(0,8),W);label("$6''$",(0,0)--(5,-1),S);
point C = (2.5,3.5);
label(rotate(-aTan(1/5))*scale(0.8)*"Happy Birthday!",C);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
415abe2c-6600-5764-b9e8-0915824f1a0d
task_key
geometry--test--415abe2c-6600-5764-b9e8-0915824f1a0d
task_revision_id
1
config / split
geometry / test

Official source

initial import