Two plots of land have the same perimeter. One is a square of side 64 m and the other is a rectangle of length 70 m. Find the breadth of the rectangular plot. Which plot has the greater area and by how much?

Given:

Side of square = 64 m

We know, Perimeter of square = 4 × side

⇒ Perimeter of square = 4 × 64 = 256 m

But, it is given that there is a rectangle of length 70 m with perimeter equal to the perimeter of this square.

Let the breadth of the rectangle be ‘b’ m.

We know, Perimeter of rectangle = 2 (length + breadth)

⇒ 256 = 2(70 + b)

⇒ 256 = 140 + 2b

⇒ 2b = 116

Thus, the breadth of the rectangular plot is 58 m.

We know, area of a square = side²

⇒ Area of square plot = 64²

∴ Area of square plot = 4096 m²

We know, area of a rectangle = length × breadth

⇒ Area of rectangular plot = 70 × 58

∴ Area of rectangular plot = 4060 m²

Clearly, square plot is bigger in area.

Difference in areas = (4096 – 4060) m² = 36 m²

Thus, the square plot has the higher area, and it is 36m² more than the area of the rectangular plot.