Answer:
Breadth is 4 m and length is 8m
Explanation:
Area of the rectangle = Length * breadth
Area of the rectangular goat pen= 32 square meters
Perimeter of the rectangular goat pen = 24 meters
Perimeter of the rectangle = 2(length + breadth)
24= 2(l+b)
12= length + breadth
12- breadth = length ----------- equation A
Area = l*b
32= l*b
32= (12- b) *b
32= 12b- b²
b²-12b+32= 0------------------- equation B
Solving the quadratic equation by factorization
b²- 8b- 4b+32= 0
b(b-8) -4(b-8)= 0
(b-8) = 0
(b-4)= 0
b= 8 or b=4
As breadth is usually smaller than length then putting b= 4 in equation A
gives
12- breadth = length
12-4= length
length = 8
Hence breadth is 4 m and length is 8m