Field Perimeter Problem
A farmer owns two fields in Rectangle shape. The area of Field A is represented by the expression x² + 7x + 12 square metres, and one side of this field is x + 4 metres long.
The area of Field B is represented by the expression 7x² + 14x square metres, and one side of this field is x + 2 metres long.
Find the total perimeter of both fields in terms of x.
Field A
Dimensions:
- Area: x² + 7x + 12
- One Side: x + 4
Field B
Dimensions:
- Area: 7x² + 14x
- One Side: x + 2
Total Perimeter of Fields in Terms of x
A farmer owns two fields:
Field A
Area: x² + 7x + 12 square metres
Length of the field A: (x + 4) metres
Breadth of the field A calculation:
- Area formula: Area = Length × Breadth
- (x + 4) × Breadth = x² + 7x + 12
- Breadth = (x² + 7x + 12) ÷ (x + 4)
- Breadth = x² + 7x + 12
x + 4 - Factorize x² + 7x + 12 ➝ (x + 4)(x + 3)
- Breadth = (x² + 7x + 12) ÷ (x + 4)=(x + 4)(x + 3) ÷ (x + 4)
- Breadth = x² + 7x + 12
x + 4 = (x + 4)(x + 3)
x + 4 - Breadth = x + 3
Dimensions of Field A:
- Length: x + 4
- Breadth: x + 3
Perimeter of Field A:
- Perimeter = 2 × (Length + Breadth)
- Perimeter = 2 × [(x + 4) + (x + 3)]
- Perimeter = 2 × (2x + 7)
- Perimeter = 4x + 14
Field B
Area: 7x² + 14x square metres
One side: (x + 2) metres
Other side calculation:
- Area formula: Area = Length × Breadth
- (x + 2) × Other side = 7x² + 14x
- Other side = (7x² + 14x) ÷ (x + 2)
- Breadth = (7x² + 14x)
(x + 2) - Factorize 7x² + 14x ➝ 7x(x + 2)
- Other side = 7x
Dimensions of Field B:
- Length: x + 2
- Breadth: 7x
Perimeter of Field B:
- Perimeter = 2 × (Length + Breadth)
- Perimeter = 2 × [(x + 2) + (7x)]
- Perimeter = 2 × (8x + 2)
- Perimeter = 16x + 4
Total Perimeter
Total Perimeter = Perimeter of Field A + Perimeter of Field B
Total Perimeter = (4x + 14) + (16x + 4)
Total Perimeter = 20x + 18 metres