The cost of levelling a rectangular field at 50 per square metre is 30,000. If its length
and breadth are in the ratio of 3: 2, then find
its perimeter.​ pls help

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 = 50/m²

The total cost of levelling the field, T = 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/U

∴ 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.

the answer will be

cosine

step-by-step explanation: