Question

Perimeter of a rectangular field 50 m long and 30 m
wide is equal to the perimeter of a square field. Find
the area of the square field.

Answer 1

Step-by-step explanation:

Length of rectangle=50m

Breadth of the rectangle=30

Perimetre of rectangle =2(L+B)

=2(50+30)

=2x80

=160 m

Perimetre of the rectangle = Perimetre of the Square

160m=160m

Perimetre of square = 4xSide

=160=4xside

=160/4=side

=Side = 40m

Area of square =SidexSide

=40x40

=1600m.sq.

PLEASE MARK TO BRAIN LIST

Answer 2

Answer

The area of the square field is 1600m²

$\bf\large{\underline{Given}}$

• The perimeter of a rectangular field is equal to the perimeter of a square field.
• The length and breadth of the rectangular field is 50m and 30m

$\bf\large{\underline{To Find :}}$

• The area of the square field

$\bf\large{\underline{Formula \: to \: be \: used : }}$

★Perimeter of a rectangle = 2(l+b)

★Perimeter of a square = 4l

★ Area of a square = l²

$\bf\large{\underline{Solution :}}$

Let us consider the length of the side of the square field be x m

$\underline{\sf\dag \: \: According \: to \: question : }$

$\sf\implies perimeter \: of \: rectangle = perimeter \: of \: square$

$\sf\implies 2(50+30) = 4x \\\\ \sf\implies 2\times 80 = 4x \\\\ \sf\implies x = \dfrac{\cancel{160}}{\cancel{4}} \\\\ \sf\implies x = 40$

Now the area of the square field is :

$\sf ↦Area \ of \ square= 40^{2} \\\\ \sf ↦ Area \: of \: square= 1600$

Therefore , the area of the square field is 1600m²