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Find the Diagonal of a Rectangle


Date: 07/26/97 at 05:16:59
From: Boyd Henderson
Subject: One very confused crew

Dr Math

I am a building contractor and one day during lunch someone asked how 
to find the diagonal of a rectangle. We use a tape measure to square 
different things on the job site by measuring corner to corner and 
then again on the opposite corners.  I have tried to think it through 
and recall some of that high school geometry but it was just too long 
ago. Could you please help? I know that it is not as tough as I am 
making it.

Thanks.

Boyd Henderson


Date: 07/26/97 at 09:17:15
From: Doctor Jerry
Subject: Re: One very confused crew

Hi Boyd,

Carpenters, whether they remember the Pythagorean Theorem or not, use 
this classical theorem when they use a tape measure to square various 
corners on the job. 

Think of the rectangle as a piece of paper.  Suppose the lengths of 
the sides are a = 8.5 by b = 11.  Draw the diagonal on the paper.  
Let its length be c. The Pythagorean Theorem (for either of the 
triangles on opposite sides of the diagonal) says that a^2+b^2=c^2  
(a^2 means a*a or a squared).

So, c^2 = 8.5^2+11^2 = 72.25+121 = 193.25.

This is c^2.  To calculate c, take the square root of 193.25, which is 
13.90, approximately.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Geometry
High School Practical Geometry
High School Triangles and Other Polygons

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