The original area of the given rectangular field be 288 ft²
Given, a rectangular field is twice as long as it is wide.
Now, if 3 feet are taken from the width and 4 feet are taken from the length then the resultant area of the field of the field be 180 ft².
We have to find the original area of the field.
Let the original length of the rectangular field be, l
and original breadth of the rectangular field be, b
Now, l = 2b
New length be, (2b - 4)
New breadth be, (b - 3)
New area be, 180
(2b - 4)(b - 3) = 180
2b² - 10b + 12 = 180
b² - 5b + 6 = 90
b² - 5b - 84 = 0
b² - 12b + 7b - 84 = 0
b(b - 12) + 7(b - 12) = 0
(b - 12)(b + 7) = 0
As, breadth can not be negative, therefore the breadth be 12 ft.
and length be 24 ft.
Original area be,
Area = 12×24
Area = 288 ft²
Hence, the original area be 288 ft²
Learn more about Areas and Perimeter here https://brainly.com/question/27430555
#SPJ4
