Question

6. 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

Solution :-

Let the length and breadth of the rectangular plot be 11x and 4x respectively

∴ Perimeter of the plot =

$\sf{⟹ \frac{total \: cost}{cost \: of \: 1meter} }$

$\sf{⟹ \frac{75000}{100} }$

$\sf{⟹ 750m}$

We know that Perimeter of rectangle = 2 (length + breadth)

Therefore, according to the question,

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

$\sf{⟹ 750 = 2 × 15x} \:$

$\sf{⟹ 750 = 30x} \:$

$\sf{⟹ X = \frac{750}{30} }$

$\sf{⟹ X = 25} \:$

Hence, length of rectangular plot

$\sf{= 11 \: x \: 25 = 275 m} \:$

And breadth of rectangular plot

$\sf{ = 4 \: x \: 25 = 100 m}$

Answer 2

Solution :-

Let the length and breadth of the rectangular plot be 11x and 4x respectively

∴ Perimeter of the plot =

\sf{⟹ \frac{total \: cost}{cost \: of \: 1meter} }⟹costof1metertotalcost

\sf{⟹ \frac{75000}{100} }⟹10075000

\sf{⟹ 750m}⟹