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

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 $c$ .

So the perimeter of the polygon would be...

$8 + 6 + a + b + c + d$

Note that $a + b = 8$ , and $c + d = 6$ .

Now we plug those in: $\begin{align*} 8 + 6 + a + b + c + d &= 8 + 6 + 8 + 6 \\ &= 14 \times 2 \\ &= 28 \\ \end{align*}$

28 is $\boxed{\text{C}}$ .

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1986 AJHSME Problems/Problem 13

Problem

Solution

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