Question

select the correct answer.
the runways at an airport are arranged to intersect and are bordered by an orange fencing as shown in the figure. a security guard needs to patrol along the fencing once per shift. what is the estimated distance they walk every shift?
image of an x (two intersecting runways) with horizontal measurement 3,000 ft and vertical measurement 4,000 ft
a. 14,000 ft
b. 7,000 ft
c. 10,000 ft
d. 20,000 ft

Explanation:

Step1: Analyze the figure (two intersecting runways, each forming a "X" shape, so we can consider the lengths of the two diagonals or the sum of the two "cross" lengths). Wait, actually, the figure is like two intersecting lines, and the fencing is along the borders. Wait, maybe each runway is a rectangle? No, the figure is an "X", so maybe each of the two runways has a length that can be found using the Pythagorean theorem? Wait, no, the given lengths are 3000 ft (horizontal) and 4000 ft (vertical). Wait, maybe the two runways are each a line segment, and the total fencing is the sum of the lengths of the two runways. Wait, but the "X" shape: if we consider the two runways, each is a line that spans the 3000 and 4000 ft? Wait, no, maybe the two runways are each a line with length equal to the hypotenuse? Wait, no, the problem says "estimated distance". Wait, maybe the two runways are each 5000 ft? Wait, no, 3-4-5 triangle: 3000, 4000, so hypotenuse is 5000. But there are two runways? Wait, no, the figure is an "X", so two runways intersecting. So the total fencing is the sum of the lengths of the two runways. Wait, but maybe each runway is a line, and the length of each runway is the hypotenuse? Wait, no, the horizontal distance is 3000, vertical is 4000. Wait, maybe the two runways are each 5000 ft? Wait, 3000-4000-5000 triangle. So each runway is 5000 ft? But no, the "X" shape: if you have two runways intersecting, forming an "X", then the total length of the fencing would be the sum of the lengths of the two runways. Wait, but maybe the runways are each a line, and the length of each runway is 5000 ft? Wait, no, the problem says "estimated". Wait, maybe the two runways are each 5000 ft? Wait, no, 3000 and 4000 are the legs, so hypotenuse is 5000. But there are two runways, so total length is 50002=10,000? Wait, no, maybe the runways are each 5000, but the options include 10,000. Wait, let's check the options. Option C is 10,000. Wait, maybe the two runways are each 5000 ft, so total is 10,000. Wait, but how? Let's think again. The figure is an "X", so two runways intersecting. The horizontal distance is 3000 ft, vertical is 4000 ft. So each runway is a line that goes from one end to the other, crossing at the center. So the length of each runway is the hypotenuse of a right triangle with legs 3000 and 4000? Wait, no, 3000 and 4000 are the horizontal and vertical distances between the ends. So the length of each runway is 5000 ft (since 3-4-5 triangle, 3000-4000-5000). Then there are two runways, so total length is 50002=10,000 ft. So the answer is C.

Step2: Wait, maybe I made a mistake. Wait, the runways are bordered by fencing. So each runway has two sides? No, the figure is an "X", so maybe the fencing is along the edges of the two runways. Wait, maybe the two runways are each a rectangle, but the figure is simplified. Alternatively, maybe the total length is the sum of the two diagonals. Wait, the horizontal distance is 3000, vertical is 4000. So the length of each diagonal (runway) is 5000, so two diagonals: 5000*2=10,000. So the estimated distance is 10,000 ft.

Answer:

C. 10,000 ft