Certainly! Let's solve this step by step.
1. Understanding the Problem:
- We have a rectangular ground.
- The length [tex]\( l \)[/tex] is three times the breadth [tex]\( b \)[/tex].
- The perimeter of the ground is 96 meters.
- We need to find the cost of growing grass on this ground at Rs 65 per square meter.
2. Formulate the Equations:
- The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[
P = 2 \times (\text{length} + \text{breadth})
\][/tex]
- Substituting the given perimeter:
[tex]\[
96 = 2 \times (l + b)
\][/tex]
- Since the length [tex]\( l \)[/tex] is three times the breadth [tex]\( b \)[/tex]:
[tex]\[
l = 3b
\][/tex]
Therefore:
[tex]\[
96 = 2 \times (3b + b)
\][/tex]
Simplifying:
[tex]\[
96 = 2 \times 4b
\][/tex]
[tex]\[
96 = 8b
\][/tex]
3. Solve for the Breadth [tex]\( b \)[/tex]:
- Isolate [tex]\( b \)[/tex] by dividing both sides of the equation by 8:
[tex]\[
b = \frac{96}{8}
\][/tex]
[tex]\[
b = 12 \, \text{meters}
\][/tex]
4. Calculate the Length [tex]\( l \)[/tex]:
- Using the relation [tex]\( l = 3b \)[/tex]:
[tex]\[
l = 3 \times 12
\][/tex]
[tex]\[
l = 36 \, \text{meters}
\][/tex]
5. Calculate the Area of the Ground:
- The area [tex]\( A \)[/tex] of a rectangle is given by:
[tex]\[
A = \text{length} \times \text{breadth}
\][/tex]
[tex]\[
A = 36 \times 12
\][/tex]
[tex]\[
A = 432 \, \text{sq. meters}
\][/tex]
6. Calculate the Cost of Growing Grass:
- The cost is given by the area multiplied by the cost per square meter:
[tex]\[
\text{Cost} = A \times 65
\][/tex]
[tex]\[
\text{Cost} = 432 \times 65
\][/tex]
[tex]\[
\text{Cost} = 28,080 \, \text{Rs.}
\][/tex]
So, the cost of growing grass on the ground is Rs 28,080.
