Question

A farmer wishes to grow 100 m² rectangular vegetable garden. Since he has with the only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of the garden.

Answer 1

Dimensions will be 10m * 10m

Answer 2

Let the length of rectangular garden is l and breadth is b.

A/c to question, Garden is fenced on three sides.

∴ l + 2b = 30

l = 30 - 2b ------(1)

Given, area of rectangular garden = 100 m²

l × b = 100

(30 - 2b)b = 100

30b - 2b² = 100

2b² - 30b + 100 = 0

b² - 15b + 50 = 0

b² - 10b - 5b + 50 = 0

(b - 10)(b - 5) = 0

b = 5 and 10

So, l = 30 - 2b ⇒l = 20 or 10

Hence, rectangular garden sides (20, 5) or (10, 10)