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A triangle has sides of following dimensions $7cm$, $17cm$ and third side is an integer. Find the number of triangles possible.

What I did:- Maximum possible value of third side

As we know, third side will be surely less than the sum of the other two sides. $23<17+7$ Minimum possible value of third side Difference of any two sides is less than the third side $11>17-7=10$

Number of possible values between $11$ and $23$ are= $13$. But the total number of triangles possible is 33. How?

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    $\begingroup$ You are correct. There is a typographical error in the answer key. $\endgroup$ – N. F. Taussig Aug 1 '17 at 18:42
  • $\begingroup$ Perhaps it would help if you told us exactly which book/website you got this problem from, and the question number/page number. $\endgroup$ – projectilemotion Aug 2 '17 at 7:20
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It looks like you're right; there's probably an error with the answer.

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Let $a$ be side-length of the third side.

Hence, $7+17>a$ and $7+a>17$, which gives $10<a<24$ or $11\leq a\leq 23$, which gives the answer: $13$.

I think your book is wrong.

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