and area are in the ratio 1:2.
3. The cost of fencing a square field at 14 per metre is 28000. Find the area of the field.
4. The length and breadth of a rectangular field are in the ratio 3:2. If the perimeter of the field is 250 m,
find the cost of reaping the field at 15 per 50 m².
Answers
(1)
Given :
- The cost of fencing a square field at ₹ 14 per m is ₹ 28000.
To Find :
The area of square.
Solution :
Here we are given the cost of fencing the field. We are the cost of per m as well as the whole field. So, by dividing the cost of fencing the total field by the cost of fencing the field per m we will get the perimeter. Now from the perimeter we will get the side of the square. And then using the formula for area of a square we will get the area.
Explanation :
We know that fencing is done in the boundary. So here we need to find the perimeter.
ATQ,
⇒ Perimeter = Cost of fencing the whole field/Cost of fencing per m
where,
- Cost of fencing the whole field = ₹ 28000
- Cost of fencing per m = ₹ 14
Substituting the values,
⇒ Perimeter = 28000/14
⇒ Perimeter = 2000
∴ Perimeter = 2000 m.
We know that,
Perimeter of square = 4 × side
where,
- Perimeter = 2000 m
⇒ 2000 = 4 × side
⇒ 2000/4 = side
⇒ 500 = side
∴ Side = 500 m.
Now,
Area of square = Side × Side
where,
- Side = 500 m
⇒ Area = 500 × 500
⇒ Area = 250000
∴ Area = 2,50,000 m².
Area of the square is 2,50,000 m².
(2)
Given :
- The length and breadth of a rectangular field are in the ratio 3:2.
- The perimeter of the field is 250 m
- The cost of reaping the field is at 15 per 50 m².
To Find :
- The cost of reaping.
Solution :
Here we will first find the length and breadth of the rectangle from the perimeter. Then we have to find the area. After that follow the steps.↓
Explanation :
Let the common ratio be “x”.
We know that,
Perimeter of rectangle = 2(Length + Breadth)
where,
- Perimeter = 250 m
- Length = 3x
- Breadth = 2x
Substituting the values,
⇒ 250 = 2(3x + 2x)
⇒ 250 = 6x + 4x
⇒ 250 = 10x
⇒ 250/10 = x
⇒ 25 = x
∴ x = 25 m.
- Length = 3x = 3 × 25 = 75 m
- Breadth = 2x = 2 × 25 = 50 m
Now,
Area of rectangle = Length × Breadth
where,
- Length = 75 m
- Breadth = 50 m
⇒ Area = 75 × 50
⇒ Area = 3750
∴ Area = 3,750 m².
Now, we can see that it is said that the cost of reaping at 50 m² is ₹ 15.
So,
ATQ,
⇒ Cost of reaping = 3750/50 × 15
⇒ Cost of reaping = 75 × 15
⇒ Cost of reaping = 1125
∴ Cost of reaping = ₹ 1,125.