Question

two plot of land have same perimeter.one is a square of side 64m and the other is a rectangle of length 70m.find tje breadth of the rectangular plot. which plot has the greater area and by how much

Answer 1

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

Solution :

We have Provided with two plot of land of same perimeter . One is a Square While the other one is a rectangle also We have given side of square and length of the rectangle 64 m  and 70 m of a rectangle respectively . We need to find which has greater area and by how much and the breadth of the rectangle  ?

*Perimeter of Square Plot*

Perimeter of Square = 4  * Side

⇒ 4 * 64

⇒ 256 m

*We Know that* ,  

Perimeter of the rectangle = 2(Length + Breadth)  

*According to the Question*

Perimeter of the rectangular plot is equal to the perimeter of square plot

*Substituting the Values in the formula*  

⇒ 2 ( 70 + b )  = 256

⇒ 70 + b = (256/2)

⇒ 70 + b = 128

⇒ b = 128 - 70

⇒ b = 58 m

*Finding area of the rectangle*

Area of the rectangle = Length * Breadth  

⇒ 70 * 58

⇒ 4060 m^2

*Finding area of the Square Plot*  

Area of Square = Side * Side  

⇒ 64 * 64

⇒ 4096 m^2

*Finding the area increased by how much*

Area of Square - Area of rectangle  

⇒ 4096 - 4060

⇒ 36 m^2  

Therefore , Area of square is Greater than area of the rectangle by 36 m^2