Question

A garden is 120 m long and 85 m wide. It has an inside path of uniform width 3.5m all around it. The remaining part of the garden is covered by grass. Find the cost of covering the garden by grass at 50 paisa per square meter.

Answer 1

Hint:Here we have to find the cost of covering the garden by grass for that we have to find the area of the rectangle for which the covering has to be done. To find the area we have to find the length and breadth of the inner garden by subtracting the length and breadth of the garden and the width of the path. Using the area formula and newly formed length and breadth. By multiplying the newly found area with the cost given we will find the required cost.

Formula used:Area of rectangle \[ = {\rm{ }}Length{\rm{ }} \times {\rm{ }}Breadth\]

Complete step-by-step answer:

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle
Complete step by step answer:
Here, it is given that the length of the outer rectangle = 120 meter and breadth of the outer rectangle=85 meter.
Let the outer rectangle be ABCD and the inner rectangle be\(abcd\).
The uniform width of the inside path is 3.5 meter all around it.
We subtract outer length from uniform width to get data about the inner shape.
So, the length of the inner rectangle is given subtracting the length of the outer field and the uniform width.
Length of the inner rectangle = 120 - 7 = 113 m
Similarly the breadth of the inner rectangle = 85 - 7 = 78 m
We know that, the formula of area of a rectangle \[ = {\rm{ }}Length{\rm{ }} \times {\rm{ }}Breadth\]
The area of the inner rectangle = 113 × 78 = 8814 m²
We have to find the cost of covering,
We know that 1 rupee = 100 paise then 50 paisa = 0.5 rupees
So, by multiplying the Rs 0.5 into the area of the inner rectangle we will find the cost of covering.
The total cost of covering the garden by grass = 0.5 × 8814= Rs 4407
Hence, the total cost of covering the field with grass is Rs. 4407

Additional Information:Area of rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a 2d shape which has four sides and four vertices. All the four angles of the rectangle are right angles. The opposite sides of the rectangle are equal and parallel to each other.

Note:Here we subtract 7m from both the length and breadth of the outer rectangle because it is given that the width of the path is 3.5m all around so in the length there will be reduction in both the sides similarly in breadth. Hence we subtract 3.5+3.5=7m from the length and breadth.