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Question -

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



Answer -

Perimeter of figure (a) = 4 × side = 4 × 60 = 240 m

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 = 40 m
Area of figure (a) = (side)2 =60 × 60 = 3600 m2
Area of figure (b) = l × b = 80 × 40 = 3200 m2
So, area of figure (a) is longer than the area of figure (b).

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