Question

Two plats of land have the same perimeter. One is a square of side 64cm and another one is rectangle of length 70cm .which plat has the greater area and by how much?

Answer 1

Given :

• Two plats of land have the same perimeter.

• One is a square of side 64cm.

• One is rectangle of length 70cm .

To find :

• The greater area and by how much = ?

Step-by-step explanation:

Perimeter of Square Plot = Perimeter of Square = 4  × Side

➮ 4 × 64

➮ 256 m

As given in the Question :

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

And We know that,

Perimeter of the rectangle = 2(Length + Breadth)  

Substituting the values in the above formula, we get,

➮ 2 ( 70 + b )  = 256

➮ 70 + b = (256/2)

➮ 70 + b = 128

➮ b = 128 - 70

➮ b = 58 m

Now

We have to find area of the rectangle,

Area of the rectangle = Length × Breadth  

Substituting the values in the above formula, we get,

➮ 70 × 58

➮ 4060 m²

Now we have to find area of the Square Plot,  

Area of Square = Side²  

Substituting the values in the above formula, we get,

➮ 64 × 64

➮ 4096 m²

Now we have to find the area increased by how much,

Hence,

Area of Square = 4096 m²

Area of rectangle  = 4060 m²

We can see that Area of square is greater than the Area of rectangle.

Now, finding the area by how much Area of square is greater than the Area of rectangle.

On Subtracting Area of rectangle from Area of square.

Area of square - Area of rectangle.

Substituting the values, we get,

➮ 4096 - 4060

➮ 36 m²  

Therefore , Area of square is greater than the Area of rectangle by 36 m²

Answer 2

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