The image appears to be the same as the previous one, but I will analyze it again to ensure everything is correct.

Problem from Image:

The problem discusses the perimeter of a rectangular field, finding its area, and includes the following details:

• Given:
  • Perimeter $= 144 \, \text{m}$
  • Length $= 48 \, \text{m}$

Tasks:

1. Find the breadth of the rectangular field.
2. Calculate the area of the rectangular field.

Step 1: Find the Breadth

The perimeter $P$ of a rectangle is given by: $P = 2 \times (\text{Length} + \text{Breadth})$ Substitute the given values: $144 = 2 \times (48 + \text{Breadth})$

Simplify the equation: $144 = 96 + 2 \times \text{Breadth}$

Subtract 96 from both sides: $48 = 2 \times \text{Breadth}$

Divide by 2: $\text{Breadth} = 24 \, \text{m}$

Step 2: Calculate the Area

The area $A$ of a rectangle is given by: $A = \text{Length} \times \text{Breadth}$ Substitute the values: $A = 48 \, \text{m} \times 24 \, \text{m} = 1152 \, \text{m}^2$

Final Answer:

1. Breadth of the field: $24 \, \text{m}$
2. Area of the field: $1152 \, \text{m}^2$

Would you like any additional details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. What would be the area if the length was increased by 50%?
2. How would you calculate the perimeter if the breadth were doubled?
3. If the length and breadth were both increased by 5 meters, what would be the new area?
4. How does the formula for the area change if you consider a square instead of a rectangle?
5. If the perimeter were reduced by 20 meters, how would this affect the length and breadth?

Tip: Always double-check your calculations by substituting the values back into the original formula. This helps confirm your results.