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MATH / A "slackrope walker" is much like a tightrope walker except that the rope on…

Problem

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

problem

A "slackrope walker" is much like a tightrope walker except that the rope on which he performs is not pulled tight. Paul, a slackrope walker, has a rope tied to two 15 m15\text{ m} high poles which are 14 m14\text{ m} apart. When he is standing on the rope 5 m5\text{ m} away from one of the poles, he is 3 m3\text{ m} above the ground. How long in meters is the rope? [asy] draw((0,0)--(14,0)--(14,15)--(5,3)--(0,15)--cycle,black+linewidth(1)); draw((0,3)--(5,3)--(5,0),black+linewidth(1)+dashed); draw((0,-3)--(6,-3),black+linewidth(1)); draw((8,-3)--(14,-3),black+linewidth(1)); draw((0,-3.5)--(0,-2.5),black+linewidth(1)); draw((14,-3.5)--(14,-2.5),black+linewidth(1)); draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black+linewidth(1)); draw((14,0)--(14,1)--(13,1)--(13,0)--cycle,black+linewidth(1)); draw(rotate(90)*Label("Paul"),(5,3),3N); label("5",(0,3)--(5,3),N); label("3",(5,0)--(5,3),E); label("14",(7,-3)); label("15",(14,0)--(14,15),E); [/asy]
Plain-text mathematical notation (without MathML)
A "slackrope walker" is much like a tightrope walker except that the rope on which he performs is not pulled tight. Paul, a slackrope walker, has a rope tied to two 15 m high poles which are 14 m apart. When he is standing on the rope 5 m away from one of the poles, he is 3 m above the ground. How long in meters is the rope?

[asy]
draw((0,0)--(14,0)--(14,15)--(5,3)--(0,15)--cycle,black+linewidth(1));
draw((0,3)--(5,3)--(5,0),black+linewidth(1)+dashed);
draw((0,-3)--(6,-3),black+linewidth(1));
draw((8,-3)--(14,-3),black+linewidth(1));
draw((0,-3.5)--(0,-2.5),black+linewidth(1));
draw((14,-3.5)--(14,-2.5),black+linewidth(1));
draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black+linewidth(1));
draw((14,0)--(14,1)--(13,1)--(13,0)--cycle,black+linewidth(1));
draw(rotate(90)*Label("Paul"),(5,3),3N);
label("5",(0,3)--(5,3),N);
label("3",(5,0)--(5,3),E);
label("14",(7,-3));
label("15",(14,0)--(14,15),E);
[/asy]
Original LaTeX notation
A "slackrope walker" is much like a tightrope walker except that the rope on which he performs is not pulled tight. Paul, a slackrope walker, has a rope tied to two $15\text{ m}$ high poles which are $14\text{ m}$ apart. When he is standing on the rope $5\text{ m}$ away from one of the poles, he is $3\text{ m}$ above the ground. How long in meters is the rope?

[asy]
draw((0,0)--(14,0)--(14,15)--(5,3)--(0,15)--cycle,black+linewidth(1));
draw((0,3)--(5,3)--(5,0),black+linewidth(1)+dashed);
draw((0,-3)--(6,-3),black+linewidth(1));
draw((8,-3)--(14,-3),black+linewidth(1));
draw((0,-3.5)--(0,-2.5),black+linewidth(1));
draw((14,-3.5)--(14,-2.5),black+linewidth(1));
draw((0,0)--(1,0)--(1,1)--(0,1)--cycle,black+linewidth(1));
draw((14,0)--(14,1)--(13,1)--(13,0)--cycle,black+linewidth(1));
draw(rotate(90)*Label("Paul"),(5,3),3N);
label("5",(0,3)--(5,3),N);
label("3",(5,0)--(5,3),E);
label("14",(7,-3));
label("15",(14,0)--(14,15),E);
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
4be65b88-3c41-5cdf-be2f-ed5590ca7a3f
task_key
prealgebra--test--4be65b88-3c41-5cdf-be2f-ed5590ca7a3f
task_revision_id
1
config / split
prealgebra / test

Official source

initial import