Question

The perimeter of a square & a rectangular plot are same 64m. If the length of the rectangular plot is 22m . Find that which plot is bigger .

Thankyou

Answer 1

Answer:

Perimeter is equal of both shapes

2(l+b)= 64= perimeter of rectangle

2(22+b)= 64

22+b= 32

b= 32-22= 10cm

perimeter of square= 4* side

64= 4* side

16= side

Area of rectangle= 10*22= 220cm²

Area of square= 16*16= 256cm²

Hence, square plot is bigger

Answer 2

Given :

• The perimeter of a square & a rectangular plot are same 64m.
• Length of the rectangular plot is 22m.

To Find :

• Plot with bigger area.

Solution :

✰ As we know that, Perimeter of Square is given by 4 × side and Perimeter of Rectangle is given by 2(Length + Breadth) . Now in this question it is given that both the plot have same perimeters and length of the rectangular plot is 22m and we have to find which plot has a bigger area. So for finding whose area is bigger we need the side of the Square plot and Breadth of the Rectangular plot. After finding the side of the Square plot and Breadth of the Rectangular plot, we will find the Areas of both the plots separately and then we will compare them.

⠀⠀⠀

⠀⠀⠀⟼⠀⠀⠀Both have same perimeter

⠀⠀⠀⟼⠀⠀⠀4 × side = 2(L + B)

⠀⠀⠀⟼⠀⠀⠀64 = 2(22 + B)

⠀⠀⠀⟼⠀⠀⠀64/2 = 22 + B

⠀⠀⠀⟼⠀⠀⠀32 = 22 + B

⠀⠀⠀⟼⠀⠀⠀32 - 22 = B

⠀⠀⠀⟼⠀⠀⠀10m = B

⠀

Thus Breadth of the rectangular plot is 10m

⠀

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Side of Square Plot :

⠀

⠀⠀⠀⟼⠀⠀⠀Perimeter = 4 × side

⠀⠀⠀⟼⠀⠀⠀64 = 4 × side

⠀⠀⠀⟼⠀⠀⠀64/4 = side

⠀⠀⠀⟼⠀⠀⠀16m = side

Thus, Side of Square Plot is 16m

⠀

Area of Square Plot :

⠀⠀⠀⟼⠀⠀⠀Area = (side)²

⠀⠀⠀⟼⠀⠀⠀Area = side × side

⠀⠀⠀⟼⠀⠀⠀Area = 16 × 16

⠀⠀⠀⟼⠀⠀⠀Area = 256m²

⠀

Thus, Area of Square Plot is 256m²

⠀

________________

Area of Rectangular Plot :

⠀

⠀⠀⠀⟼⠀⠀⠀Area = Length × Breadth

⠀⠀⠀⟼⠀⠀⠀Area = 22 × 10

⠀⠀⠀⟼⠀⠀⠀Area = 22 × 10

⠀⠀⠀⟼⠀⠀⠀Area = 220m²

⠀

Thus, Area of Rectangular Plot is 220m²

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So, Square Plot has a bigger area than that of Rectangular Plot.

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