Question

Two plots of land have the same perimeter. One is square in shape with side 50m, and the other is rectangular with a breadth of 15m. Which of the plots has a greater area and by how much?

Answer 1

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Plots have same perimeter.

Side of square field = 64m

perimeter = 64*4 = 256m

length of rectangular plot = 70m

breadth = b

2(70+b) = 256

⇒ 70+b = 256/2 = 128

⇒ b = 128 - 70

⇒ b = 58m

Area of square = 64*64 = 4096 m²

Area of rectangle = 70*58 = 4060 m²

Area of square is more than rectangle by = 4096 - 4060 = 36m²

Answer 2

Answer:

Square plot has greater area and by 1225 sq. m.

Step-by-step explanation:

Side of square = 50 m.

Perimeter of Square = 4S = 4 * 50 = 200 m.

Breadth of rectangle = 15 m.

Length of rectangle = L m.

Perimeter of Rectangle = 2(L+B) = 200 => 2(L + 15 ) = 200 => L + 15 = 100

=> L = 85 m.

Area of Square = Side² =  50² = 2500 sq. m.

Area of Rectangle = L * B = 15 * 85 = 1275 sq. m.

Thus the Square plot has greater area and by 1225 sq. m.