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Mathematics-Online problems:

Interactive Problem 155: Climbing up a Pyramid

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
On a pyramid having a square base and edge length $ a$ a path ascends from one of the bottom vertices to the apex at a slope of $ 25\, \%$.


\includegraphics{pyramide}


Determine the height $ h$ of the pyramid, the length $ c$ of the first section of the path, the lengths $ b$ and $ a',$ as well as the total length $ L$ of the path, all of them in terms of $ a.$

Hint: Let the slope here be the ratio of the difference in altitude to the distance covered (i.e. $ f:g$ in the drawing below).


\begin{picture}(2217,708)(664,-523)\thicklines \put(676,-511){\line( 1, 0){20... ...1){\makebox(0,0)[lb]{$f$}} \put(1581, -60){\makebox(0,0)[lb]{$g$}} \end{picture}


Answer:

$ h$ =   $ a$
$ c$ =   $ a$
$ b$ =   $ a$
$ a'$ =   $ a$
$ L$ =   $ a$

(The results should be correct to three decimal places.)


   

(From: Day of Mathematics 1996)
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  automatically generated: 8/11/2017