Answer

Correct Answer : b ) 4 cm

Let the Rectangles be A and B.

Let the lengths of A and B be l_A and l_B respectively.

Let the breadths of A and B be b_A and b_B respectively.

It is given that,

Area of rectangles A and B = l_A* b_A = l_B* b_B = 480 square cm.

Difference between the lengths of A and B = l_A- l_B = 6 cm ...........................(1)

Here, as we can see that the product of length and breadth is the same for both the rectangles and the lengths and breadths for both the rectangles are different.

Suppose we assume the length of rectangle A to be more than that of rectangle B. In that case, it is evident that the breadth of A is less than that of B because the product of both the lesser quantities will make the resultant lesser, but here we require a similar resultant in terms of area.

Difference between the breadths of A and B = b_B - b_A = 4 cm ...........................(2)

We need to find the difference between the perimeters of both rectangles.

Perimeter of rectangle A = 2 * (l_A + b_A)  ...........................(3)

Perimeter of rectangle B = 2 * (l_B + b_B) ...........................(4)

In equation 1 and equation 2, we can write

l_A = l_B + 6

b_B -  4 = b_A

Let's add both equations, we get

l_A + b_A = l_B + 6 + b_B - 4

l_A + b_A = l_B + b_B + 2

Let's multiply by 2 on both sides.

2 * (l_A + b_A) = 2 * (l_B + b_B) + 4

From eq. 3 and eq. 4, we get,

Perimeter of A = Perimeter of B + 4

The difference between the perimeters of rectangles A and B is 4 cm.

Important Conclusion

Here, it is important to note that the area of the rectangles played no role in deciding the difference between the perimeters.

We can deduce a result that if the area of two rectangles is equal and their breadths and lengths differ by x and y respectively. Then the difference between the perimeters of the rectangles will be twice the difference between x and y.

Hence, (b) is the correct answer.