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प्रश्न
The perimeter of a rectangular plot is 300m. It has an area of 5600m2. Taking the length of the plot as x m, calculate the breadth of the plot in terms of x, form an equation and solve it to find the dimensions of the plot.
उत्तर
The length of the rectangle = x m
Let the breadth of the rectangle = b m
The perimeter of a rectangle with length l and breadth b = P = 2(l + b)
The perimeter of a triangle with length x and breadth b = 2(x + b) = 300
⇒ (x + b) = 150
⇒ b = 150 - x
The area of a rectangle with length l and breadth b = A = l x b
The area of a rectangle with length x and breadth (150 - x)
= X x (150 - x)
= 5600
⇒150x - x2 = 5600
⇒ x2 - 150x + 5600 = 0
⇒ x2 - 80x - 70x + 5600 = 0
⇒ x(x - 80) - 70(x - 80) = 0
⇒ (x - 80)(x - 70) = 0
⇒ x = 70m, 80m
When breadth = 70m, then the length
= 150 - 70
= 80m
When breadth = 80m, then the length
= 150 - 80
= 70m.
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