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

Answer:

=Perimeter of square=

4 × side

60 × 4

240m

=Perimeter of rectangle=

2(length+breadth)

2(80+breadth)

160+2b = 240(it is given that perimeter of square and rectangle is same)

2b=240-160

2b = 80

b=80/2

b= 40m

=area of (a)

side×side

60×60

3600m²

=area of (b)

length×breadth

80×40

3200m²

area of square field is larger

Answer 2

$\sf{Side \: of \: a \: square = 60 m (Given)}$

$\sf{And \: the \: length \: of \: rectangular \: field, \: l = 80 m \: (Given)}$

$\sf{According \: to \: question,}$

$\sf{Perimeter \: of \: rectangular \: field \: ⟹ Perimeter \: of \: square \: field}$

$\sf ⟹ 2(l+b) = 4×Side (using \: formulas)$

$\sf{⟹2(80+b) = 4×60}$

$\sf{⟹160+2b = 240}$

$\sf{⟹b = 40}$

$\sf{Breadth \: of \: the \: rectangle \: is \: 40 m.}$

$\sf{Now, \: Area \: of \: Square \: field}$

$\sf⟹ {side}^{2}$

$\sf⟹ {60}^{2}$

$\sf⟹ {3600m}^{2}$

$\sf{And \: Area \: of \: Rectangular \: field}$

$\sf{⟹Length×breadth}$

$\sf{ ⟹ 80×40}$

$\sf ⟹ \: {3200}^{2}$

$\sf{Hence , \: Area \: of \: Square \: field \: is \: larger.}$