How Much Material to Purchase?

Date: 11/01/97 at 16:58:05
From: kim peterson
Subject: Ramp

Sanchez warehouse wants to install a 3-foot wide ramp from the level 
floor to the top of the 4-foot high platform. A regulation states that 
for every 2 feet that such a ramp rises vertically, the bottom of the 
ramp must be placed 5 feet farther from the bottom of the platform.  
If the material for the top surface of the ramp comes in 3-foot widths 
and whole-foot lengths, what is the minimum length of the material 
that must be purchased?

Date: 11/03/97 at 10:23:10
From: Doctor Pipe
Subject: Re: Ramp

Kim,

A good way to understand this problem and its solution is to draw a 
picture. 

Draw the picture so that each half inch that you draw represents one 
foot in the problem - the line representing the four feet from the 
floor to the platform will be two inches long).

Start by drawing a horizontal line to represent the floor. Then draw a 
vertical line up from the floor to represent the four feet from the 
floor to the platform. Finally, draw another horizontal line from the 
top of the vertical line to represent the platform. Label the floor, 
the platform, and the four feet from the floor to the platform.

Now, the regulation says that for each two feet that a ramp rises 
vertically, the bottom of the ramp must be placed 5 feet from the 
bottom of the platform.  Since our ramp needs to rise four feet, the 
bottom of the ramp needs to be 10 feet from the bottom of the 
platform. Measure and mark the spot on your drawing that is on the 
floor ten feet from the bottom of the platform (remember that each 
half inch in your drawing represents a foot in the problem). Now draw 
a straight line from the edge of the platform to the point on the 
floor. This line represents a ramp built to comply with the 
regulation.

Notice that you have drawn a right triangle. To calculate the length 
of the ramp, apply the Pythagorean theorem. The ramp is the 
hypotenuse, the length of the floor under the ramp (10 feet) is the 
length of one leg, and the height of the platform (4 feet) is the 
other leg.

When writing down your final answer, remember that the material for 
the top of the ramp is sold only in whole-foot lengths. This means 
that you can't buy 10.77 feet. If you need 10.77 feet of material then 
you have to buy twelve feet.

You'll also want to sweep the ramp each hour so no one slips on it!

-Doctor Pipe,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/