Question

1. A square and a rectangular field with measurements as given in the figure have the
same perimeter. Which field has a larger area?​

Answer 1

Question ::-

A square and a rectangular field with measurements as given in the figure have the

same perimeter. Which field has a larger area?

Given ::-

• Two fields are given [ square and rectangle ]

• side of square = 60m

• Length of rectangle = 80m

• The perimeter of square and rectangle field is equal.

To find ::-

• Which field has a larger area ?

Solution ::-

• side of square = 60m

Perimeter of square = 4 × side

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 4 × 60

Perimeter (square) = 240

___________

• Length of rectangle = 80 m

$⟼$ Perimeter of rectangle = 2 ( length+ Breadth )

$⟼$ perimeter of square = perimeter of rectangle

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[ given ]

$⟼$ 2 ( length+ Breadth ) = 240

$⟼$ 2 ( 80 + b ) = 240

$⟼$ ( 80 + b ) = $\dfrac{240}{2}$

$⟼$ 80 + b = 120

$⟼$ b = 120 - 80

$⟼$ b = 40m

__________

Area of Square (a)

= ${(side)}^{2}$

= 60 × 60

= 3600 ${m}^{2}$

_______

Area of figure (b)

= l × b

= 80 × 40

= 3200 ${m}^{2}$

_________

So, area of figure (a) is longer than the area of figure (b).