A rectangular goat pen has an area of 32 square meters and a perimeter of 24 meters. What are the dimensions of the pen?

Answer:

Breadth is 4 m and length is 8m

Step-by-step 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

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