Problem 292; An Easy Solution

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John Nolton
Posts: 15

Joined: 10/11/2011 Problem 292; An Easy Solution Flag »  Reply » The solution that Lindell put forth for problem 292 is long and more complicated than need be. To solve this problem you need to know 3 things. 1. Heron's formula 2. Pythagorean relation 3.The formula for the altitude (alt) of a general triangle #1. the area of triangle ABC is K (area)= sqrt s(s-a)(s-b)(s-c) where s= 1/2(a+b+c)      (this is Heron's formula) #3. Alt = 2K/side AC #2. If you don't know this look it up. Solve for the Area of triangle ABC; s=1/2(6+5+7) , therefore  s= 9 K= sqrt 9(9-5)(9-6)(9-7),  K= 14.696938457 Now Alt of triangle ABC= (2*14.696938457)/7 , therefore Alt= 4.199125273 If we call the foot of the Alt from B to line AC "E" then you will solve 2 triangles using the Pythagorean relation. First we will solve for distance EC in triangle BEC , EC = sqrt 5^2-Alt^2 , EC=2.714285714. Now solve for "x" (distance BD in the problem) using the Pathagorean relation again, DE= 3-EC = 0.285714286 , so x= sqrt DE^2+4.199125273^2; x= 4.208834246 Note: calculations were done on an HP20S calculator and took less than one minute for the solution to the whole problem. John Nolton Tombstone, AZ
Sunday, April 6, 2014 at 1:27:55 PM
20171214yuanyuan
Posts: 152

Joined: 12/14/2017 Re: Problem 292; An Easy Solution Flag »  Reply »

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Thursday, December 14, 2017 at 1:03:39 AM
20171214yuanyuan
Posts: 152

Joined: 12/14/2017 Re: Problem 292; An Easy Solution Flag »  Reply »

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Thursday, June 14, 2018 at 9:59:29 PM
annajohnsn
Posts: 73

Joined: 3/18/2019 Re: Problem 292; An Easy Solution Flag »  Reply » This website is very useful for students like me. washington dc tour We all know the importance of maths in our education system. This site helps the students to learn maths in a very interest way. All the doubts can be discussed here and hence can be solved. I loved the site very much.
Monday, May 20, 2019 at 6:14:28 AM

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