CBSE Class 10 Answered

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.