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 the rate Rs 100 per metre it will cost

the village panchayat Rs 75, 000 to fence the plot. What

are the dimensions of the plot?​







5 points waiting!!

Answer 1

Step-by-step explanation:

Perimeter = 75000/100 = 750

Perimeter of rectangle = 2(length + breadth)

=2(11x + 4x)

=30x

30x = 750

x = 25

11 * 25 = 275

4 * 25 = 100

Therefore,

Length = 275m

Breadth = 100m

Answer 2

Answer:

✩ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.5,2){\sf{\large{4x}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\sf{\large{11x}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

⠀

☢ Given : At the rate Rs 100 per metre it will cost the village panchayat Rs 75,000 to fence the plot.

⠀

$:\implies\sf Cost\:of\:fencing=Perimeter \times Rate\\\\\\:\implies\sf Rs.\:75000 = Perimeter \times Rs.\:100\:m^{ - 1}\\\\\\:\implies\sf \dfrac{Rs.\:75000}{Rs.\:100 \:m^{ - 1}} = Perimeter\\\\\\:\implies\sf Perimeter = 750\:m$

⠀⠀⠀$\rule{160}{0.8}$

Let the Length be 11x and Breadth be 4x of Rectangular Plot.

☯ $\underline{\boldsymbol{Perimeter\:of \:the\: Rectangluar\:Plot :}}$

$\dashrightarrow\sf\:\: Perimeter=2(Length+Breadth)\\\\\\\dashrightarrow\sf\:\:750 =2(11x + 4x)\\\\\\\dashrightarrow\sf\:\:750 = 2 \times 15x\\\\\\\dashrightarrow\sf\:\:750 = 30x\\\\\\\dashrightarrow\sf\:\: \dfrac{750}{30} = x\\\\\\\dashrightarrow\sf\:\:x = 25$

$\rule{180}{1.5}$

$\underline{\bigstar\:\textsf{Dimensions of the Rectangular Plot :}}$

$\bullet\:\:\textsf{Length = 11x = 11(25) = \textbf{275 m}}\\\bullet\:\:\textsf{Breadth = 4x = 4(25) = \textbf{100 m}}$