How many triangles can be constructed so that lengths of the sides are three consecutive odd integers and the perimeter is less than 1000?

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Raghunathan Narasimhan

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Maths and Physics for IIT-JEE & Physics for NEET

let the sides are x,x+2,x+4 ,x being an odd integer then , x+(x+2)+(x+4)<1000 , i.e, 3x<994 ,x being an odd integer ,max value of x can be 331.....now x can be any odd no from 1 to 331...like 1,3,5,7,..............,329,331...and for every such x,you will get 1 triangle..(options form an arithmetic progression)......331=1+(n-1)2,...
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let the sides are x,x+2,x+4 ,x being an odd integer then , x+(x+2)+(x+4)<1000 , i.e, 3x<994 ,x being an odd integer ,max value of x can be 331.....now x can be any odd no from 1 to 331...like 1,3,5,7,..............,329,331...and for every such x,you will get 1 triangle..(options form an arithmetic progression)......331=1+(n-1)2, which gives n=116...so 116 possible triangles satisfy your conditions!!!! read less
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Let the sides be x,x+2,x+4 ,x being an odd integer then , x+(x+2)+(x+4)<1000 , i.e, 3*x<994 ,x being an odd integer. Max value of x can 331 Now x can be any odd no from 1 to 329...like 1,3,5,7,..............,331 and for every such x, you will get one triangle.. From arithmetic progression......331=1+(n-1)*2,...
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Let the sides be x,x+2,x+4 ,x being an odd integer then , x+(x+2)+(x+4)<1000 , i.e, 3*x<994 ,x being an odd integer. Max value of x can 331 Now x can be any odd no from 1 to 329...like 1,3,5,7,..............,331 and for every such x, you will get one triangle.. From arithmetic progression......331=1+(n-1)*2, i.e. (n-1)*2 = 330 (n-1) = 165 n=166 which gives n=166 So 166 possible triangles read less
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Physics & Maths

165 @Neel, @Vikas, @ Raghunathan... U need to remove one case 1,3,5 as it cannot form sides of a triangle (since sum of two sides cannot be less than third side)
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Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

NO. OF POSSIBLE TRIANGLES = 166
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Maths and Physics for IIT-JEE & Physics for NEET

let the sides are x,x+2,x+4 ,x being an odd integer then , x+(x+2)+(x+4)<1000 , i.e, 3x<994 ,x being an odd integer ,max value of x can be 331.....now x can be any odd no from 1 to 331...like 1,3,5,7,..............,329,331...and for every such x,you will get 1 triangle..(options form an arithmetic progression)......331=1+(n-1)2,...
read more
let the sides are x,x+2,x+4 ,x being an odd integer then , x+(x+2)+(x+4)<1000 , i.e, 3x<994 ,x being an odd integer ,max value of x can be 331.....now x can be any odd no from 1 to 331...like 1,3,5,7,..............,329,331...and for every such x,you will get 1 triangle..(options form an arithmetic progression)......331=1+(n-1)2, which gives n=166...so 166 possible triangles satisfy your conditions!!!! read less
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Which Coaching Institute provides best study Material for Mathematics of class 12?
IIT Junction in Wakad Pune will get you the best material for your preperation
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As IIT & board exams are coming near , students you are free ask any doubt in PCM boards or IIT/BITSAT . I completely understand the pressure , anxiety at this time. But maintain calm at this time & be happy .Don't take any stress and just keep on studying with the flow . Truly speaking the person who is studying till the end with happiness only crack these competitive exams easily. Many students leave studying in the last due to tension or piling of massive course. One suggestion for these students is, whatever will going to happen in future is not in your hands , what really in your hands is --> this time !! so just give your best in this time and forget everything else. Don't feel that others have studied more than me, or they have been studying from 2 years or starting , because anything can happen in the last , this is a true fact !! It's about your processor not Harddisk meaning it's about how your brain run at that time in the exams , not specifically about how much you have stored. I myself have seen many people who have got very good ranks by just studying properly in last two months over those students who have been studying for 2 years continously . So remain motivated and give whatever you have to your studies . But very important thing remain happy and enjoy studies. I will be telling other tips & tricks to complete maximum portion in the last in less time . Keep tuned to my future posts.
As a chance to prove yourself and evaluated by a traditional way to the student. Student should not fear but make .
Harshil Garg
How can one get 90% and above in the CBSE class 12 board without any coaching and tuition?
Be upto date in reading and learning lessons. You need compressive reading and little bit practise of questions. Read.. read... read... the lessons as many time as possible and try to recall as much as possible. You can get 90% and above surely.
Nageswara
I am IIT DELHI B.TECH Graduate .Highly Interested in teaching IIT JEE aspirants specially MATHS, PHYSICAL CHEMISTRY, PHYSICS with excellence in teaching.
Planning to intensify iit jee coaching starting next batch. Why dont you call me up, so that we harmonise our efforts to success.
Salman Khan
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