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

Asked by  | 20th Mar, 2013, 10:18: PM

Expert Answer:

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.

Answered by  | 21st Mar, 2013, 10:30: AM

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