The length of a rectangular landing strip exceeds its width by 3,700 feet. If its perimeter is 17,400 feet, what is the length, in feet, of the airfield?
A. 2500
B. 5000
C. 6200
D. 10000
E. 13700
P = 2L + 2W
17,400 = 2(W + 3700) + 2W
17,400 = 4W + 7400
10,000 = 4W
2,500 = W
Let:
L = length of the landing strip (in feet)
W = width of the landing strip (in feet)
We are given that the length of the landing strip exceeds its width by 3,700 feet, so we can say:
L = W + 3,700
We are also given that the perimeter of the landing strip is 17,400 feet. The perimeter of a rectangle is calculated by adding the lengths of all four sides, so we can set up the equation:
2L + 2W = 17,400
Substituting L with its value in terms of W, we have:
2(W + 3,700) + 2W = 17,400
Simplifying the equation:
2W + 7,400 + 2W = 17,400
4W + 7,400 = 17,400
4W = 10,000
W = 10,000 / 4
W = 2,500
Now that we have the width of the landing strip, we can substitute this value back into the equation for L:
L = W + 3,700
L = 2,500 + 3,700
L = 6,200
Therefore, the length of the airfield is 6,200 feet. So the correct answer is option C.