Question

The length and breadth of a rectangular garden are in the ratio 7:3. If the area of the field
is 525 m², then find the cost of fencing it at * 75 per m.

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Answer 1

★ Given:

The length and breadth of a rectangular garden are in the ratio 7:3.

Area of the field is 525 m².

Cost of fencing per m² is Rs 75.

★ To Find:

The total cost of fencing.

★ Solution:

Let the length and breadth of the rectangle be 7x and 3x.

Formula for area of a rectangle = lb

lb = 525 m²

7x x 3x = 525 m²

21x² = 525 m²

x² = 525/21

x² = 25

So x = √25

x = 5

Therefore length = 7x = 7 x 5 = 35 m

Breadth = 3x = 3 x 5 = 15 m

Perimeter of a rectangle = 2 (l + b)

Perimeter = 2 x (35 + 15)

Perimeter = 2 x 50

Perimeter = 100 m

Cost of fencing per m = Rs 75

So total cost of fencing = 100 x 75

= Rs 7500

Therefore the total cost of fencing the rectangular garden is Rs 7500.

Important Perimeter and Area Formulae:

→ Rectangle

✳ Perimeter = 2 (l + b)

✳ Area = lb

→ Square

✳ Perimeter = 4a

✳ Area = a²

→ Circle

✳ Perimeter = 2πr

✳ Area = πr²