Question

The perimeter of a rectangular field is 82m and its area is 400m2, find the dimension of the rectangular field. 

Answer 1

Area of rectangular garden with sides a and b = 400 = ab 

⇒ a = `400/"b"` ....(i)

Perimeter of rectangular garden with sides a and b = 82 = 2a + 2b 

⇒ a + b = 41 ... (ii)

Putting (i) in (ii), we get 

⇒ `400/"b" + "b" = 41`

⇒ b² - 41b + 400 = 0 

⇒ b² - 25b - 16b + 400 = 0 

⇒ b (b -25) - 16 (b - 25) = 0

⇒ (b - 25) (b - 16) = 0 

⇒ b = 25 or 16. 

Putting this in (i), we get, a= 16 or 25 

Hence two sides of the rectangle are 16 and 25.