Gopi has a square field of side 75 m. Narayan has a rectangular field

1.	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» 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

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»

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