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UKMT Intermediate Mathematical Challenge, 2019

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows a triangle with sides $n^2 + n$ , $2n + 12$ and $3n + 3$ . What is the sum of all the values of $n$ for which the triangle is isosceles?

(A) $7$ (B) $9$ (C) $12$ (D) $13$ (E) $16$

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