A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide...

Question

A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?

Answer 1

a 9 feet wide hall way makes a right turn into a 6 feet wide hallway

how long a pipe can be carried through the turn?

it may help to draw a diagram

use quadrant I, with the orign where the two hallways connect, the corner

then diagonally across is the point (9,6) where the other sides of the 2 hallways meet

draw a 45 degree line through the point (9,6)

it will intersect the axes at (18,0) and (0,12)

find the length of that line segment = sqr(468) = about 21.6 feet = maximum length of the pipe that can navigate around the corner (ignoring how high the hallways are)

find the hypotenuse of a right trianlge with sides 18 and 12

h^2 = 18^2 +12^2

h^2 = 324+144 = 468

h =sqr468= 2sqr117 = a little more than 21.6 feet