Question

room.
8. The length and breadth of a rectangular piece of land are in the ratio of 5:3. If the total cost
of fencing it at 24 per metre is 9600, find its length and breadth.​

Answer 1

Answer:

The length and breadth of a rectangle in ratio = 5:3

Total cost of fencing = ₹9600

Rate of fencing = ₹24 per metre

Perimeter = 9600/24

= 400

the length = 5x

breadth = 3x

Perimeter = 2(l+b)

400 = 2(5x+3x)

400 = 2 × 8x

400 = 16x

400/16 = x

25 = x

So, the length of a rectangle = 5×25 = 125

the breadth of a rectangle = 3×25 = 75

Answer 2

Answer:

The length and breadth of the rectangle are 125m and 75m respectively.

Explanation:

Given

• The land is in the shape of a rectangle
• Its length and breadth are in the ratio 5:3.
• The cost of fencing the land at Rs 24/m is Rs 9600.

To Find

• The length of the land.
• The breadth of the land.

Solution

First, we will find the perimeter of the land. As the rate of fencing and the cost of fencing is given. We can easily find its perimeter.

Let "p" be the length of the perimeter of the rectangular land.

land that can be fenced with 24 Rs = 1m

Land that can be fenced with Rs 9,600:

Total price of fencing the land / price of fencing 1 metre

⟹ 9600/24

⟹ 400

400 metres is the perimeter of the land.

Now, let the common Factor between the length and the breadth of the land is "x".

The length of the land = 5x

The breadth of the land = 3x

Perimeter of a rectangle = 2 (Length + Breadth)

⟹ 400 m = 2 (Length + Breadth)

⟹ 400m = 2( 5x + 3x )

⟹ 400m/2 = 5x + 3x

⟹ 200m = 5x + 3x

⟹ 200m = 8x

⟹ 200m/8 = x

⟹ 25m = x

The length of the land:

⟹ 5x

⟹ 5( 25m )

⟹ 125m

The breadth of the land:

⟹ 3x

⟹ 3( 25m)

⟹ 75m

The length and breadth of the rectangle are 125m and 75m respectively.