Mrs. Kukreti wants to make a kitchen garden behind her house in a rectangular plot by using the Bio-fertilizer. For this she has done fencing by a wire of 105 m around the three sides of the plot ahd fourth side is covered by the wall of her house. The area of the plot is increased by 50 square meters, if the length of the plot is decreased by 5 m and breadth of the plot is increased by 5 m. Find the dimensions of the plot.
Answers
Answer:
The dimensions of the rectangular plot are : length = 45 m, breadth = 30 m
• Let the length of the rectangular plot be taken as l, and the breadth be taken as b.
Given,
Length of the wire used for fencing three sides of the plot = 105 m
• Since the plot is fenced on three sides, one of its sides is open along the length (Fig. 1).
• Perimeter of a rectangle is given as 2 (length + breadth).
• Now, according to the question,
Perimeter of the plot = perimeter of the fence + length of the open side of plot
• Therefore,
2 ( l + b ) = 105 m + l
Or, 2l + 2b = 105 m + l
Or, 2l - l + 2b = 105 m
Or, l + 2b = 105 m -(i)
• Now, the area of a rectangle is given as (length × breadth).
Therefore, area of the rectangular plot = l × b = lb
• Length of the plot on decreasing the value by 5 m = l - 5 m
Breadth of the plot on increasing the value by 5 m = b + 5 m
Therefore, new area of the plot = (l - 5m) (b + 5m)
= lb + 5l m - 5b m - 25 m²
• According to the question,
lb + 50 m² = lb + 5l m - 5b m - 25 m²
Or, lb + 50 m² = lb + 5l m - 5b m - 25 m²
Or, lb - lb + 50 m² + 25 m² = (5l - 5b) m
Or, 75 m² = 5 (l - b) m
Or, l - b = 75 m² / 5 m
Or, l - b = 15 m -(ii)
• Now, multiplying eq. (ii) with 2, we get,
2 (l - b) = 2 × 15 m
=> 2l - 2b = 30 m -(iii)
• Adding eq. (iii) with (i), we get,
(iii) + (i)
=> (l + 2l) + (2b - 2b) = (105 + 30) m
=> 3l + 0 = 135 m
=> 3l = 135 m
=> l = 135 m / 3
=> l = 45 m
Therefore, length (l) = 45 m
• Putting the value of l in eq. (ii), we get,
45 m - b = 15 m
=> 45 m - 15 m = b
=> b = 30 m
Therefore, breadth (b) = 30 m
• Bio-fertilizers are advantageous over chemical fertilizers in many ways . Some of them are :
(i) Bio-fertilizers are made of organic components, and therefore, do not degrade the quality of soil or deplete it of its nutrients when applied to crops or plants.
(ii) Bio-fertilizers are cost-effective as they are available at prices cheaper than that of chemical fertilizers in the market.
(iii) Bio-fertilizers are environment-friendly and have minimal polluting effect on the environment, unlike chemical fertilizers.
