Area of a Right TriangleDate: 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/ |
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