Mathematics
The perimeter of a rectangular plot is 130 m and its area is 1000 m2. Take the length of the plot as x metres. Use the perimeter to write the value of breadth in terms of x. Use the values of length, breadth and area to write an equation in x. Solve the equation and calculate the length and breadth of the plot.
Answer
Given,
Perimeter = 130 m
Area = 1000 m2
Length = x meters
Let breadth = b meters
Perimeter = 2(length + breadth)
⇒ 130 = 2(x + b)
⇒ x + b = 65
⇒ b = 65 - x
Area = length × breadth
⇒ 1000 = x × (65 - x)
⇒ 1000 = 65x - x2
⇒ x2 - 65x + 1000 = 0
⇒ x2 - 40x - 25x + 1000 = 0
⇒ x(x - 40) - 25(x - 40) = 0
⇒ (x - 40) (x - 25) = 0
⇒ x = 40 or x = 25
If x = 40 then,
Length = x = 40 m
Breadth = 65 - x = 65 - 40 = 25 m
If x = 25 then,
Length = x = 25 m
Breadth = 65 - x = 65 - 25 = 40 m
Generally we consider length > breadth
Hence, length = 40 m and breadth = 25 m.
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