Question

A rectangular garden is 65 m long and 50 m wide. Two cross paths each 2 m wide are to be
constructed parallel to the sides. If these paths pass through the centre of the garden, find
the cost of constructing the paths at the rate of 69 per m'2.

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Answer 1

Answer:

Rs 15594

Step-by-step explanation:

Area of 1st path =65×2=130

Area of 2nd path =50×2=100

Area of the interaction of the path =2×2=4

Area covered by the path =130+100-4=226

COST =226×69=Rs 15594

Answer 2

Given: length of the garden = 65m

Width of the garden = 50m

Width of the paths = 2m

Rate of construction = ₹69/m²

The paths are parallel to the sides and move through the center

To Find: rate of construction of the paths

Solution:

Since the paths need to be parallel to the sides and move through the center, they should be mutually perpendicular and one parallel to each side of the rectangle.

Let us consider path 1 to be parallel to the width

Length of path 1(l1) = 50 m

Width of path 1 (w1) 2m

Area of a rectangle = length x width

Area of path 1 = 50 x 2

                       = 100 m²

Let us consider path 2 to be parallel to the length

Length of path 2 (l2) = 65m

Width of path 2 (w2) = 2m

Area of path 2 = 65 x 2

                         = 130 m²

In the center, there is an overlapping which is formed by a square of side 2m. This area is common for both the paths and hence will be constructed once. We have to subtract this area from the total area to be constructed.

Area of square = side x side

Overlapping area = 2 x 2

                              = 4 m²

Total area to be constructed = Area of path 1 + Area of path 2 - Overlapping area

Total area to be constructed = 100 + 130 - 4

                                                = 226 m²

Cost of construction = Area to be constructed x Cost of construction per m²

Cost of construction = 226 x 69

                                  = ₹ 15594

Therefore, the cost of the construction of the paths is ₹ 15594.