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The Perimeter of a Triangle

The bisector drawn from vertex $N$ of triangle $M N P$ divides side $M P$ into segments of 28 and 12.

Find the perimeter of triangle $M N P$, given that $M N - N P = 18$.

#
Apply the property of the bisector of a triangle.

## Solution

By the property of the bisector of a triangle, the sides are proportional to 28 and 12. Since $28-12=16$, the coefficient of proportionality is $9 / 8$. Therefore, the perimeter is $(9 / 8+1)(28+12)=85$.

## Answer

85.