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a person has a rectangular garden whose area is 100 sq m. he fences three sides of the garden with 30 m barbed wire. on the fourth side, the wall of his house is constructed, find the dimensions of the garden.
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 – 30b + 100 = 0

? 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 × 10 = 30 – 20 = 10

When b = 5, we have

l = 30 – 2b = 30 –2 × 10 = 30 – 10 = 20

Thus, the dimension of the garden is 10 m × 10 m or 20 m × 5 m.


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