Question

A farmer prepares rectangular vegetable garden of area 180 sq meters. With 39 meters of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden. 

Answer 1

Let the length and breadth of the rectangular garden be x and y meter, respectively.

Given:   

xy = 180 sq m   ...(i)  and 

2y + x = 39 

⇒ x = 39 – 2y 

Putting the value of x in (i), we get: 

(39 – 2y)y = 180 

⇒ 39 – 2y² = 180 

⇒ 39y – 2y² – 180 = 0 

⇒ 2y² – 39y + 180 = 0

⇒ 2y² – (24 + 15)y + 180 = 0 

⇒ 2y² – 24y – 15y + 180 = 0 

⇒ 2y(y – 12) – 15(y – 12) = 0 

⇒ (y – 12)(2y – 15) = 0 

⇒ y = 12 or y = `15/2 = 7.5` 

If y = 12, x = 39 – 24 = 15 

If y = 7.5, x = 39 – 15 = 24 

Thus, the length and breadth of the garden are (15 m and 12 m) or (24 m and 7.5 m), respectively.