Question

3. There is a narrow rectangular plot. The length and breadth of the plot are in the ratio of 11:4. At the rate of Rs. 100
per meter it will cost village panchayat Rs.75000 to fence the plot. What are the dimensions of the plot?
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Answer 1

Given:-

• Length and breadth of the plot are in the ratio = 11:4
• At the rate of Rs.100 per meter it will cost the village panchayat Rs.75,000 to fence the plot.

To find:-

• Dimensions of the plot

Required Formula:-

• Perimeter of rectangle = 2(l + b)

Solution:-

Where,

• length = 11x meter
• breadth = 4x meter

Then,

$\\ :\implies\sf{Perimeter =2(11x + 4x) } \\ \\ :\implies\sf{Perimeter = 2(15x)} \\ \\ :\implies\sf{Perimeter = 30x}$

Now,

• Finding the value of x by putting the value of cost of fencing and perimeter mutilplied by rate of per meter

$\\ :\implies\sf{75000 = 30x \times 100} \\ \\ :\implies\sf{ \frac{750 \cancel{00}}{1 \cancel{00}} = 30x} \\ \\ :\implies\sf{750 = 30x} \\ \\ :\implies\sf{x = \frac{ \cancel{75} \cancel{0}}{ \cancel{3} \cancel{0}}} \\ \\ :\implies \underbrace{ \boxed{\frak{x = 25}}} \: \blue{ \bigstar}$

Therefore,

• Length = 11 × 25 = 275 meter
• Breadth = 4 × 25 = 100 meter

Hence,

• The length of the plot is 275 m and breadth of plot is 100 m.

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