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 100 per metre it will
cost the village panchayat 75000 to fence the plot. What are the dimensions of
the plot?​

Answer 1

Given:

• The length and breadth of the rectangular plot are in the ratio 11:4
• At the rate 100 per metre it will cost the village panchayat 75000 to fence the plot.

To Find:

• Dimensions of the plot

Solution:

Let length of plot be = 11x

And breadth of plot be = 4x

Now

Perimeter of rectangular plot :-

$\leadsto$ 2( Length + Breadth)

$\leadsto$ 2( 11x + 4x )

$\leadsto$ 2(15x)

$\leadsto$ 30x

Now

According to question:

Total cost of fencing the plot = Rs 75,000/-

Cost of fencing 1 metre = Rs 100/-

Cost of fencing 30x metres :-

$\leadsto$ 30x × 100

$\leadsto$ Rs 3000x/-

Comparing total cost of fencing the rectangular plot :-

$\leadsto$ 3000x = 75,000

$\leadsto$ x = 25

Now

Dimensions of plot :-

Length of plot = 11x = 11(25) = 275m

Breadth of plot = 4x = 4(25) = 100m

Hence, required dimensions of plot are 275m and 100m.

Answer 2

S o L u T i O n :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{4x}}}\put(7.7,1){\large{B}}\put(8.7,0.7){\matsf{\large{11 x}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

⠀

Let the Length and Breadth of the rectangular plot be 11x and 4x respectively.

A/Q,

• At the rate 100 per metre it'll cost the village panchayat 75000 to fence the plot. Costing can be done with all sides of rectangular plot, i.e Perimeter.

P E R I M E T E R :

$\bf{\dag}\;\boxed{\sf{Perimeter_{\:(rectangle)} = 2\Big(Length + Breadth \Big)}}$

• Length is 11x
• Breadth is 4x

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

$\rule{250px}{.3ex}$

⠀

C O S T⠀O F⠀F E N C I N G :

• At the rate of 100 per metre, it'll cost the village to fence the rectangular plot at 75000.

$\bigstar\;\boxed{\sf{Cost = Perimeter \times Rate}}$

$:\implies\sf 75000 = 30x \times 100 \\\\\\:\implies\sf 75000 = 3000x\\\\\\:\implies\sf x = \cancel\dfrac{75000}{3000} \\\\\\:\implies\underline{\boxed{\frak{\pink{x = 25}}}}\;\bigstar$

Hence,

• Length of the rectangular plot, 11x = 11(25) = 275 metre.
• Breadth of the rectangular plot, 4x = 4(25) = 100 metre.

$\therefore{\underline{\sf{Hence, \; length\;and\; breadth\;of\; plot\:are\;\bf{ 275\;m\;\&\;100\;m}.}}}$