Finding the Area of a Rectangle Using Ratio and Perimeter

Let's say the length and breadth of a rectangle are in the ratio 3:2. If its perimeter is 730 cm, how can we find the area of the rectangle? This problem integrates the concepts of ratios, perimeters, and areas. By following a logical and systematic approach, we can solve such problems effectively.

Step 1: Define the Dimensions

The first step is to define the dimensions based on the given ratio. Let the length of the rectangle be 3x and the breadth be 2x, where x is a common factor. This representation allows us to express both the length and breadth in terms of a single variable, which simplifies the calculations.

Step 2: Calculate the Perimeter

Using the formula for the perimeter of a rectangle, we can write:

P  2(length   breadth)

Substituting the given lengths and breadths into the formula:

P  2(3x   2x)  1

Given that the perimeter is 730 cm, we set up the following equation:

1  730

Solving for x:

x  730 / 10  73

Step 3: Find the Dimensions

Now that we know the value of x, we can determine the actual dimensions of the rectangle:

Length  3x  3 * 73  219 cmBreadth  2x  2 * 73  146 cm

Step 4: Calculate the Area

Finally, we can calculate the area of the rectangle using the formula:

Area  length * breadth

Substituting the dimensions we found:

Area  219 cm * 146 cm  31974 cm2

Therefore, the area of the rectangle is 31974 cm2.

Conclusion

This problem exemplifies the application of mathematical concepts such as ratios, perimeters, and areas in practical scenarios. By understanding the relationships between these concepts, we can solve complex problems step by step. The key takeaway is to methodically break down the problem, simplify the known parameters, and then use the relevant formulas to arrive at the solution.