Answer:
The perimeter of a rectangular field is 100 meters
Step-by-step explanation:
The given data of the rectangular field are;
The unit cost of levelling the rectangular field, U[tex]_c[/tex] = 50/m²
The total cost of levelling the field, T[tex]_c[/tex] = 30,000
The length to breadth ratio of the field, L:B = 3:2
Where;
L = The length of the field
B= The breadth of the field
From the given data of the field, we have;
The area of the field, A = T[tex]_c[/tex]/U[tex]_c[/tex]
∴ A = 30,000/(50/m²) = 600 m²
The area of the field, A = 600 m²
The formula for the area of a rectangle, A = Length, L × Breadth, B
A = L × B
We are given that the length to breadth ratio of the field, L:B = 3:2
∴ L/B = 3/2
L = (3/2) × B
The area of the rectangular field, A = L × B
∴ The area of the rectangular field, A = (3/2) × B × B = (3/2) × B²
A = (3/2) × B²
From the calculation for the cost of levelling the field, we have, A = 600 m²
∴ A = (3/2) × B²
A = 600 m²
By transitive property, we have;
(3/2) × B² = 600 m²
B² = (2/3) × 600 m² = 400 m²
B = √(400 m²) = 20 m
The breadth of the field, B = 20 m
From L = (3/2) × B, we have;
L = (3/2) × B
∴ L = (3/2) × 20 m = 30 m
∴ The length of the field, L = 30 m
The perimeter, 'P', of a rectangle given the length, 'L' and breadth, 'B', is given as follows;
The perimeter of a rectangle, P = 2·L + 2·B
Therefore, for the rectangular field, we have;
P = 2 × 30 m + 2 × 20 m = 60 m + 40 m = 100 m
The perimeter of a rectangular field, P = 100 m.
