MathDB

Triangle

ABC

has side lengths

AB=120

BC=220

, and

AC=180

. Lines

\ell_{A}

\ell_{B}

, and

\ell_{C}

are drawn parallel to

\overline{BC}

\overline{AC}

, and

\overline{AB}

, respectively, such that the intersection of

\ell_{A}

\ell_{B}

, and

\ell_{C}

with the interior of

\triangle ABC

are segments of length

55

45

, and

15

, respectively. Find the perimeter of the triangle whose sides lie on

\ell_{A}

\ell_{B}

, and

\ell_{C}

Problem Statement