Answer:
length = 75 ft and width = 25 ft
Step-by-step explanation:
Let W = width of rectangle
Let L = length of rectangle
Area of a rectangle = L x W
Perimeter of a rectangle = 2L + 2W
Therefore, if the perimeter is 200 ft then:
2L + 2W = 200
2(L + W) = 200
L + W = 100
L = 100 - W
If the Area is 1875 ft² then: 1875 = L x W
Substitute the equation for L found above: 1875 = (100 - W) x W
Expand the brackets: 1875 = 100W - W²
Subtract 1875 from both sides: 100W - W² - 1875 = 0
Swap signs: W² - 100W + 1875 = 0
Factorize: (W - 25)(W - 75) = 0
Therefore, W = 25 or 75
If W = 25, then L = 100 - 25 = 75
If W = 75, then L = 100 - 75 = 25
Therefore, as length > width, length = 75 ft and width = 25 ft
