Question

Gopi has a square field of side 75 m. Narayan has a rectangular field of length 85 m. If the perimeters of both the fields are same, whose field has greater area and by how much?

Answer 1

Side of squared field of Gopi = 75 m 

and area = 75 × 75 = 5625 sq. m 

and perimeter = 4 × side = 4 × 75 = 300 m 

Length of rectangular field of Narayan 85 m 

and b = a m (let) then

 Area = 85 × a = 85a sq. m and 

Perimeter= 2 (l + b) = 2 (85 + a) m 

According to question, both perimeter are equal 

∴ 2 (85 + a) = 300 

⇒ (85 + a) = 300/2 = 150 

⇒ a = 150 – 85 = 65 

Thus, breadth of field = 65 m then, 

area = 85 × 65 = 5525 m 

∵ 5625 > 5525 and 5625 – 5525 = 100 

∴ Area of Gopi’s field is more by 100 sq. m