Question

The area of a square is 49 sq cm A rectangle has the same perimeter as the square. If the length of the rectangle is 9.3 cm, what is its breadth? Also find which has greater area?

Answer 1

Area of square = a²
Side ( a ) = 7 cm

Given perimeter of the rectangle has same perimeter as same as square.
Length = 9.3

4a = 2( l + b )  [ l = length , b = breadth ]
28 = 2l + 2b
28 - 18.6 = 2b
9.4 = 2b
4.7 = b

Now area of the rectangle = l × b
                                      = 9.3 × 4.7
                                      = 43.71 cm²

So clearly area of rectangle is greater.

Answer 2

Let x be the breadth of the rectangle.
As area of square is 49 cm^2, its side is 7 cm.
Perimeter of square = 28 cm.
Perimeter of rectangle = 2(9.3 + x) = 28 cm
Thus, x = 4.7 cm
Are of rectangle = 4.7 * 9.3 = 43.71 cm^2
Thus, the square has greater area.