Question

Two plots of land have the same perimeter. one is square in shape with side 50 M, and the other is is rectangle with a breath of 15m .
which of the plot has a greater area and by how much?
Answer : !!
This lesson is is m e n s u r a t i o n

Answer 1

Answer:

If the side of the square is 50m

Perimeter=50×4=200

Area, 50×50=2500

If perimeter is 200 and breadth is 15, So length is

200÷15=13.3

So, Area=15×13=195

Square has more area

Step-by-step explanation:

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Answer 2

Given :

• Two plats of land have the same perimeter.

• One is a square of side 50 m.

• One is rectangle of breadth 15 m .

To find :

• The greater area and by how much = ?

Step-by-step explanation:

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

Substituting the values in the above formula, we get,

➮ 4 × 50

➮ 200 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 ( 15 + b )  = 200

➮ 15 + b = (200/2)

➮ 15 + b = 100

➮ b = 100 - 15

➮ b = 85 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,

➮ 15 × 85

➮ 1, 275 m²

Now we have to find area of the Square Plot,  

Area of Square = Side²  

Substituting the values in the above formula, we get,

➮ 50 × 50

➮ 2500 m²

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

Hence,

Area of Square = 2500 m²

Area of rectangle  = 1275 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,

➮ 2500 - 1275

➮ 1,225 m²  

Therefore , Area of square is greater than the Area of rectangle by 1,225 m².