Question

There is a narrow rectangular plot reserved for a school in mahuli village. the length and breadth of the plot are in the ratio 11:4.At rate of ₹100 per metre it will cost the village panchayat ₹75000 to fence the plot .what are the dimensions of the plot

Answer 1

$\sf\large\underline{Given:}$

$\tt{\implies Ratio\:_{(length\:and\: breadth)}=11:4}$

$\tt{\implies Rate\:_{(per\:m}=Rs.100}$

$\tt{\implies Total\:cost\:_{(fencing)}=Rs.75000}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies Plot\:_{(dimensions)}=?}$

$\sf\large\underline{Solution:}$

• At first calculate calculate the perimeter of plot than calculate it's dimension. Here perimeter of plot is perimeter of rectangle ]

$\tt{\implies Perimeter\:_{(plot)}=\frac{Total\:cost\:of\: fencing}{fencing\:rate\:per\:m}}$

$\tt{\implies Perimeter\:_{(plot)}=\dfrac{75000}{100}}$

$\tt\green{\implies Perimeter\:_{(plot)}=750m}$

• Now calculate it's dimensions here]

$\tt{\implies Let\:the\: dimensions\:of\:be\:x}$

$\tt{\implies Let\:the\: length\:of\:plot=11x}$

$\tt{\implies Let\:the\: breadth\:of\: plot=4x}$

• By applying formula here]

$\tt{\implies Perimeter\:_{(plot)}=2(length+breadth)}$

$\tt{\implies 2(11x+4x)=750}$

$\tt{\implies 2(15x)=750}$

$\tt{\implies 15x=375}$

$\tt{\implies x=25}$

• Now calculate length and breadth here]

$\tt{\implies The\: length\:of\:plot=11x}$

$\tt{\implies The\: length\:of\:plot=11(25)}$

$\tt\red{\implies The\: length\:of\:plot=275m}$

$\tt{\implies The\: breadth\:of\: plot=4x}$

$\tt{\implies The\: breadth\:of\: plot=4(25)}$

$\tt\purple{\implies The\: breadth\:of\: plot=100m}$

$\sf\large{Hence,}$

$\bf{\implies Plot\:_{(dimensions)}=275m\:and\:100m}$

$\tt{\underbrace{Answer-length=275m\:and\: breadth=100m}}$

Answer 2

Question:

There is a narrow rectangular plot reserved for a school in mahuli village. the length and breadth of the plot are in the ratio 11:4.At rate of ₹100 per metre it will cost the village panchayat ₹75000 to fence the plot .what are the dimensions of the plot

Solution

Perimeter=75000/100=750

let

Length=11x

breadth=4x

Perimeter=2(l+b)

750=2(11x+4x)

750=30x

x=25

therefore,

length=11x=>11×25=>275m

breadth=4x=>4×25=>100m