Question

has a larger area?
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

$\huge\mathfrak{\red{answer}}$

"A" has the larger area

$\underline\bold\pink{step \: by \: step \: explination}$

perimeter of figure "A" = 4×side=4×60=240m

perimeter of figure "B" = 2(L+B)

perimeter of figure "B" = perimeter of figure "A"

$2(l + b) = 240 \\ 2(80 + b) = 240 \\ 80 + b = 120 \\ b = 120 - 80 = 40m$

Area of figure "A" = (side)² = 60×60 = 3600m²

Area of figure "B" = L×B = 80×40=3200m²

So, Area of figure "A" is larger than the area of figure "B"

Answer 2

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 :-

• Length of square = 60m

• Length of rectangle = 80m

• both shapes have same perimeter

To find :-

• Which field has a larger area?

Solution :-

Perimeter of figure (a) square

= 4 × side

= 4 × 60

= 240 m

Perimeter of figure (b) rectangle

= 2 [l + b]

Perimeter of figure (b) = Perimeter of figure (a)

⇒ 2[l + b] = 240

⇒ 2 [80 + b] = 240

⇒ 80 + b = 120

⇒ b = 120 – 80

= 40 m

____________

Area of figure (a)

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

$= 60 \times 60$

$= 3600 {m}^{2}$

Area of figure (b)

= l × b

= 80 × 40

= $3200 {m}^{2}$

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