Question

cherry hills airport has a security fence that goes all the way around the airport. here is a picture of the airport. image of the airport with labeled lengths: 3 km, 3 km, 1 km, 2 km, 4 km how long is the security fence? blank kilometers submit work it out

Explanation:

Step1: Identify horizontal lengths

The total horizontal length: The bottom side is \(3 + 2=5\) km (since the top has a segment of 3 km and 2 km, and horizontally they should sum to the same as the bottom). So both top and bottom horizontal sides sum to \(5\times2 = 10\) km? Wait, no, let's do it properly. Let's "unfold" the L - shaped figure into a rectangle. The horizontal length: the bottom is \(3 + 2=5\) km. The vertical length: the right side is 4 km, and the left side has a part of 3 km and the "notch" which is 1 km, so total vertical length is \(4\) km (since when we unfold, the vertical sides: the left side is 3 km, and the notch's vertical part is 1 km, but when calculating perimeter, we can use the rectangle method. Wait, the perimeter of a rectangle is \(2\times(\text{length}+\text{width})\). Let's find the length and width. The horizontal total: \(3 + 2 = 5\) km. The vertical total: \(3+1 = 4\) km? Wait, no. Wait, the right side is 4 km, and the left side: the lower part is 3 km, and the upper part (the notch) is 1 km, so total vertical length is 4 km (since \(3 + 1=4\)). So the figure is equivalent to a rectangle with length \(5\) km (horizontal) and width \(4\) km (vertical). Then the perimeter of a rectangle is \(2\times(\text{length}+\text{width})\). So \(2\times(5 + 4)=2\times9 = 18\)? Wait, no, wait. Wait, let's calculate each side:

Top side: The top has two segments: 3 km and 2 km, so total top length: \(3 + 2=5\) km.

Bottom side: same as top, 5 km.

Left side: the left has two vertical segments? Wait, no. Wait, the left side: the lower part is 3 km, and the upper part (the notch) is 1 km? Wait, no, the figure: let's list all sides.

Left side: 3 km (vertical down - up? Wait, no, the left side is a vertical side of 3 km. Then there is a horizontal side of 3 km (right), then a vertical side of 1 km (up), then a horizontal side of 2 km (right), then a vertical side of 4 km (down), then a horizontal side of \(3 + 2=5\) km (left) back to the start? Wait, no, that's not right. Wait, let's do it step by step.

List all the outer sides:

1. Bottom: horizontal, length \(3 + 2=5\) km (from left - most to right - most bottom).

2. Right: vertical, length 4 km (from bottom - most right to top - most right).

3. Top: horizontal, length \(3 + 2=5\) km (from right - most top to left - most top, but wait, the top has a notch. Wait, no, the top: the right part is 2 km (horizontal left), then a vertical down of 1 km? No, the figure is:

- Start at the bottom - left corner.

- Move right 3 km (bottom horizontal).

- Move up 1 km (vertical).

- Move right 2 km (top horizontal).

- Move down 4 km (vertical right).

- Move left 5 km (bottom horizontal? No, wait, the bottom horizontal from right - most bottom to left - most bottom is \(3 + 2=5\) km.

Wait, maybe a better way: the perimeter of a polygon is the sum of all its outer sides. Let's use the "rectangle with a notch" but the notch doesn't affect the perimeter? Wait, no, when you have a notch, the perimeter actually increases, but in this case, the notch is a "reentrant" angle, but in this figure, the notch's horizontal and vertical sides: the horizontal side of 3 km (right), vertical side of 1 km (up), horizontal side of 2 km (right) - but when calculating perimeter, the two horizontal sides (3 km and 2 km) and the vertical side of 1 km: wait, no, the perimeter is the sum of all outer edges. Let's calculate each edge:

1. Bottom edge: length \(3 + 2=5\) km (from (0,0) to (5,0)).

2. Right edge: from (5,0) to (5,4): length 4 km.

3. Top - right horizontal edge: from (5,4) to (3,4): length 2 km (left).

4. Top - right vertical edge: from (3,4) to (3,3): length 1 km (down).

5. Top - left horizontal edge: from (3,3) to (0,3): length 3 km (left).

6. Left edge: from (0,3) to (0,0): length 3 km (down).

Now sum all these lengths:

Bottom: 5

Right: 4

Top - right horizontal: 2

Top - right vertical: 1

Top - left horizontal: 3

Left: 3

Sum: \(5+4 + 2+1+3+3=18\) km.

Alternatively, using the rectangle method: if we consider the figure as a rectangle with length \(5\) (3 + 2) and width \(4\) (3 + 1), then the perimeter of the rectangle is \(2\times(5 + 4)=18\) km. Because the "notch" (the 1 km vertical and the 3 km and 2 km horizontal) when folded, the perimeter remains the same as the rectangle, because the horizontal and vertical sides of the notch are included in the perimeter calculation as if it were a rectangle.

So the perimeter is \(2\times(5 + 4)=18\) km.

Step2: Calculate the perimeter

Using the rectangle perimeter formula \(P = 2\times(l + w)\), where \(l = 5\) km (horizontal length) and \(w = 4\) km (vertical length).

\(P=2\times(5 + 4)=2\times9 = 18\) kilometers.

Answer:

18