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Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > How many triangles can be constructed so that lengths...
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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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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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