Question

The length and breath of a rectangular piece of land are in the ratio of 5:3.If the total cost of fencing it at rs. 24 per metre is 9600rs.find the length and breath.

Answer 1

Solutions :-

Let the length and breath of a rectangular piece of land be 5x and 3x respectively.


Find the perimeter of land :-

Rs 24 = 1 m
Rs 9600 = 9600/24 = 400 m

So, Perimeter of the rectangular piece of land = 400 m


According to the question,

Perimeter of rectangle = 2(Length + Breadth)
=> 400 = 2(5x + 3x)
=> 400/2 = 8x
=> 200/8 = x = 25


Therefore,
Length = 5x = 5 × 25 = 125 m
Breadth = 3x = 3 × 25 = 75 m

Answer 2

ANSWER:

_________________________________

The length and breadth of the rectanglur piece of land are in the ratio 5:3........(given)

$let \: x \: be \: the \: common \:multiple \: of \: this \: ratio$
Therefore,

$length \: of \: the \: rectangle = 5x \: \\ breadth \: of \: the \: rectangle = 3x$
As the question is about fencing the rectangular piece of land we are suppose to find the perimeter of the rectangle.
___________________________

Total cost of painting the total field is Rs 9,600 at the rate of Rs 24 per metre
So,
$perimeter = \frac{total \: cost \: \: of \: fencing \: }{cost \: required \: to \: fence \: 1m} \\ perimeter = \frac{9600}{24} = 400m$
___________________________

Now we have the perimeter of the rectanglur piece of land and we can also know find the length and breadth of the rectanglur piece of land using the formula of perimeter of rectangle[2(l+b)]
__________________________

So,

$perimeter \: = 2(length + breadth) \\ 400 = 2(5x + 3x)\\ \\ 400 =2( 8x) \\ \frac{400}{2} = 8x \\ 200 = 8x \\ \frac{200}{8} = x \\ x = 25$
___________________________

Therefore,

$length \: of \: the \: rectangular \: piece \: of \: land = 5x = 5 \times 25 = 125m \\ \\ breadth \: of \: the \: rectangular \: piece \: of \: land = 3x = 3 \times 25 = 75m$
____________________________

So, Length =125m
and Breadth =75m

____________________________