Question

ratio of length to breadth of a rectangular park is 5:3. the cost fencing is 2400 at rs.6 per m. find the park's length

Answer 1

Answer: Length = 125m

Explanation:

Let: Length = x ; Breadth = y
Fencing = Perimeter = 2x+2y
Cost of fencing = Price per m X Perimeter
2400 = 6 X (2x+2y)
2400 = 12x + 12y (First Equation)

Ratio = x:y = 5:3
Change ratio to fraction form = x/y = 5/3
Make y as the subject:
y = 3x/5 (Second Equation)

Substitute y=3x/5 into First Equation
2400 = 12x + 12(3x/5)
[ 2400 = 12x +36x/5 ] X 5 ---> Eliminate the denominator by multiplying the whole equation by 5

12000 = 60x + 36x
12000 = 96x
x = 12000/96
x = 125

Therefore, the length is 125m

Answer 2

`{\boxed{\textsf {Length \ of \ the \ park = 125 \ m}}}`

Explanation:

To determine the length of park, first we have to calculate the perimeter of the park.

As per the question we have - ratio of length to breadth of a rectangular park is 5:3. Let's consider the length of the rectangular park be '5x' and breadth be '3x'.

The total cost of fencing = Perimeter × cost per m.

`\sf {2400 = Perimeter * 6}`

`\sf {Perimeter = (2400)/(6)}`

`\bf {Perimeter = 400 \ m }`

Perimeter of the rectangle is calculated by 2(Length + breadth), now substitute the value of perimeter in the above formula:

`\sf {2(5x + 3x) = 400 }`

`\sf {2 * 8x = 400}`

Dividing both sides by 2

`\sf {8x = 200}`

`\bf {x = 25}`

Hence the required value of (x) is 25 ,now substitute the value of x in the length of the rectangular park i.e 5x

`\sf {Length = 5x}`

`\sf {Length = 5 *25}`

`\bf {Length = 125 \ m}`

• Therefore, The Length of the park is 125 m