Question

1. The length and breadth of a rectangular piece of land are in the ratio 5:2. If the total
cost of fencing it at Rs. 12.5 per meter is Rs. 25000, find its length and breadth.
2. Find the area of a path 2m wide laid inside along the boundary of a rectangular park
of dimension 100m X 60 m. Find the cost of gravelling it at the rate of Rs. 30 per
square metre.
3. Find the area of a walking 1 m in width laid outside on all sides of a lawn of length 70
m and breadth 50 m.
4. A square garden has an area of 2500 sq.m. A part of uniform width of 2.5m runs
around it on the inside. Find the cost of laying it at Rs. 25 per sq.m.​

Answer 1

Answer:

1.)

₹12.5 is the cost of fencing = 1m

₹ 1 is the cost of fencing = 1/12.5 m

₹ 25000 is the cost of fencing= 25000/12.5 m

= 2000m

Let the length and breadth be 5x and 2x

According to the problem,

2( 5x +2x) = 2000

=> 7x = 1000

=> x= 1000/7

Therefore,

length = 5x = (5×1000)/7 = 714.29 m (approx)

breadth = 2x = (2×1000)/7 = 285.71 m (approx)

2.)

•Length of inner field=100-4=96m

•Breadth of inner field=60-4=56m

•Area of outer field=100×60=6000m^2

•Area of inner field=96×56=5376m^2

•Now, Area of the boundary=6000-5376=624m^2

•So, the cost of gravelling=624×30=Rs18720.

3.)

Area of the walking path path is 244m^2

4.)

Area of a square garden = 2, 500 m².

Length of the side of the garden =  √2,500 = 50 m.

Width of the path = 2.5 m.

Path is inside the garden.

Width of the garden that is inside (enclosed) by the path:

          50 - 2 * 2.5 = 45 m.

Length of the garden inside by the path :  = 45 m.

So the area of garden inside the path = 45 * 45 m²

       = 2, 025 m².

Area of the path = 2, 500 - 2, 025 

      = 475 m².

Cost of laying the path = Rs 25 /m² * 475 m²

     = Rs 11, 875.