Question

Two plots have the same perimeter. One is a square of 10 m and another is a breadth of 8m. Which plot has the greater area and by how much?​

Answer 1

Answer :

• Square plot has the greater area by 4m²

Given :

• One is a square of 10m
• Breadth of rectangle is 8m

To find :

• which plot has the greater and by how much

Solution :

Given ,

• Sides is 10m
• Breadth of rectangle = 8m

Perimeter of square = Perimeter of rectangle

As we know that,

• Perimeter of square = 4(side)
• Perimeter of rectangle = 2(l + b)

where , l is length , b is breadth 8m and s is side 10m

》4(side) = 2(l + b)

》4(10)m = 2(l + 8) m

》4 × 10 / 2 = l + 8

》20 = l + 8

》l = 20 - 8

》l = 12m

Hence , Length of rectangle is 12m

Now we have to find the area of square plot and area of rectangular plot

(1) Area of plot (Square) :

As we know that,

• Area of square = (side)²

》 10 × 10 m

》 100m²

Hence Area of square plot is 100m²

(2) Area of plot (Rectangle) :

As we know that,

• Area of rectangle = length × breadth

》( 12 × 8 )m

》96 m²

Hence , Area of rectangular plot is 96m²

so,

• 100 > 96

Then,

• Square plot has the greater area by 4m²

Answer 2

Given :

• Two plot have the same perimeter. One is a square of 10 m and another is a breadth of 8m.

To Find :

• Which plot has the greater area and by how much ?

Solution :

✰ As we know that, Area of Rectangle is given by Length × Breadth. So we need the length of the Rectangle to find the area of Rectangle. Now, it is given in the Question that Square plot's perimeter = Rectangle plot's perimeter. Therefore :

⠀⠀

⟹ Both have same perimeter

⟹ 4 × Side = 2 (L + B)

⟹ 4 × 10 = 2 (L + 8)

⟹ 40 = 2 (L + 8)

⟹ 40 / 2 = L + 8

⟹ 20 = L + 8

⟹ 20 - 8 = L

⟹ 12 = Length

⠀⠀

Now,

➟ Area of Square Plot :

• Area = (side)²
• Area = side × side
• Area = 10 × 10
• Area = 100m²

⠀⠀

➟ Area of Rectangular Plot :

• Area = Length × Breadth
• Area = 12 × 8
• Area = 96m²

⠀

➟ Plot with bigger area :

• On comparing the areas we get to know that Area of Square plot is bigger than that of Area of Rectangular Plot. Now we will minus Area of Rectangular Plot from Area of Square plot to find how much it is bigger.
• Bigger area - smaller area
• 100 - 96
• 4m

Thus Area of Square Plot is bigger than that of Area of Rectangular Plot by 4m

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