Answer :
Final answer:
To solve for the length and width of the runway, we can set up two equations based on the given information. By solving these equations, we find that the length of the runway is 4300 meters and the width is 80 meters.
Explanation:
To solve this problem, we can set up two equations based on the given information. Let's denote the width of the runway as w and the length as l. The first equation we can write is l = 50w + 1500, which represents the length being 1500 meters longer than 50 times its width. The second equation we can write is 2(l + w) = 11160, which represents the perimeter of the runway being 11160 meters.
Using these two equations, we can solve for the values of w and l. Substituting the first equation into the second equation, we get 2((50w + 1500) + w) = 11160. Simplifying this equation gives us: 102w + 3000 = 11160. Subtracting 3000 from both sides of the equation gives us: 102w = 8160. Dividing both sides of the equation by 102 gives us: w = 80.
Now that we have the value of w, we can substitute it back into the first equation to solve for l. Using the first equation, we get l = 50(80) + 1500 = 4300. Therefore, the length of the runway is 4300 meters and the width is 80 meters.
