1986 AJHSME Problems/Problem 13

Problem

The perimeter of the polygon shown is

$[asy] draw((0,0)--(0,6)--(8,6)--(8,3)--(2.7,3)--(2.7,0)--cycle); label("$6$",(0,3),W); label("$8$",(4,6),N); [/asy]$

$\text{(A)}\ 14 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 28 \qquad \text{(D)}\ 48$

$\text{(E)}\ \text{cannot be determined from the information given}$

Solution

Note: I'm assuming all concave angles are right angles.

At first, we may immediately put down E, because of course we don't know many of the segments. But let's give it a shot.

For the segments parallel to the side with side length 8, let's call those two segments $a$ and $b$ , the longer segment being b, the shorter one being a.

For the segments parallel to the side with side length 6, let's call those two segments $c$ and $d$ , the longer segment being d, the shorter one being c.