A certain field is a rectangle with a perimeter of 900
feet. The length is 184
feet more than the width. Find the width and length of the rectangular field.
Let x be the width of the rectangle.
Perimeter = 2(length + width)
900 = 2( x + (x+184) )
900 = 2(2x + 184)
900 = 4x + 368
4x = 532
x = 133
So the width of the rectangle is 133 ft and the length is 133+184 = 317 ft.
Let's assume that the width of the field is "w" feet.
According to the problem, the length is 184 feet more than the width. So, the length can be expressed as "w + 184" feet.
The formula for the perimeter of a rectangle is 2(length + width). Since we know the perimeter is 900 feet, we can set up the following equation:
2(w + w + 184) = 900
Simplifying the equation, we get:
2(2w + 184) = 900
4w + 368 = 900
Subtracting 368 from both sides, we get:
4w = 532
Dividing both sides by 4, we get:
w = 133
Therefore, the width of the rectangular field is 133 feet.
To find the length, we can substitute the value of the width (w) we just found into the equation for the length:
Length = w + 184 = 133 + 184 = 317
Therefore, the length of the rectangular field is 317 feet.