Question

The perimeter of the semi-circular garden is equal to the perimeter of the rectangular field whose length and breadth is x m and (x – 12) m, respectively.  If the area of the rectangle field is 1260 m². Then, find the cost of fencing of the semi-circular garden at the rate of Rs. 15 per m?

1. Rs. 2200
2. Rs. 2160
3. Rs. 2450
4. Rs. 2340
5. None of these

Answer 1

Correct Answer - Option 2 : Rs. 2160

Given:

Perimeter of the semi-circular garden = Perimeter of the rectangular field

Length of rectangular field = x m

Breadth of rectangular field = (x – 12) m

Cost of fencing = Rs. 15 per m

Formula Used:

Perimeter of semi- circular garden = πr + 2r

Perimeter of rectangular field = 2(length + breadth)

Area of rectangular field = length × breadth

Calculation:

Area of rectangular field = 1260

⇒ x(x – 12) = 1260

⇒ x² – 12x – 1260 = 0

⇒ x² – 42x + 30x – 1260 = 0

⇒ (x – 42)(x + 30) = 0

⇒ x = 42

∴ Length of rectangular field = 42 m

Breadth of rectangular field = 42 – 12 = 30 m

Perimeter of semi circular garden = Perimeter of rectangular field = 2(30 + 42)

⇒ 2× 72

⇒ 144 m

So, the cost of fencing the semi – circular garden = 144 × 15

⇒ Rs. 2160