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Area of a Right Triangle


Date: 02/09/2002 at 19:12:15
From: Chris Pierce
Subject: Geometry

Find the area of a right triangle that has a perimeter of length 16 
meters and a hypotenuse with length 7 meters.

a)sqrt56 m(sq)  b)8 m(sq)  c)10 m(sq)  d)16 m(sq)  e)none

Please show work.
Thanks.


Date: 02/10/2002 at 00:18:57
From: Doctor Schwa
Subject: Re: Geometry

Hi Chris,

This is a very nice question!

If you let a and b be the two legs of the triangle, and c = 7 is the
hypotenuse,

then the given facts become:

     a + b + 7 = 16, 
so 
     a + b = 9, and
     a^2 + b^2 = 7^2.

You want to find the area, which is 1/2 ab.

There's a nice trick for finding ab here without having to solve the 
system of equations: if you compare (a+b)^2, which is 81, with 
(a^2 + b^2), which is 49, you'll be able to solve for ab quite 
quickly.

Enjoy,

- Doctor Schwa, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra
High School Geometry
High School Triangles and Other Polygons

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