Question

A person has a rectangular garden whose area is 100 sq m.He fences 3 sides with 30m barbed wire.On the fourth side,the wall of his house is constructed.Find dimensions of the garden.

Answer 1

Let the length and breadth if the rectangle be l m and b m respectively. Suppose the person builds his house along the length of the garden.
Given, Area of the rectangular garden = 100 m2
? lb = 100 ...(1)
Length of the barbed wire = 30 m
The barbed wire is fenced along the three sides of the garden,
? l + 2b = 30
? l = 30 - 2b ...(2)
From (1) and (2), we get
(30 - 2b) b = 100
?30b - 2b 2 = 100
? b 2 -15b + 50 = 0
? b 2 -10b -5b + 50 = 0
? b(b -10) - 5(b -10) = 0
? (b - 10) (b - 5) = 0
? b - 10 = 0 or b -5 = 0
? b = 10 or b = 5
When b = 10, we get
l = 30 - 2b = 30 -2 x 10 = 30 -20 = 10
When b = 5, we have
l = 30 - 2b = 30 - 2 x 5 = 30 - 10 = 20
Thus, the dimension of the garden is 10 m x 10 m or 20 m x 5 m.