1986 AJHSME Problems/Problem 13

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Problem

The perimeter of the polygon shown is

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

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

Solution

Solution 1

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

Solution 2

Clearly the perimeter of the requested region is the same as the perimeter of the rectangle with the dashed portion. This makes the answer obviously $2(6+8)=28\rightarrow \boxed{\text{C}}$

1986 AJHSME (Problems • Resources)
Preceded by Problem 12	Followed by Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

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