Question

The length and the breadth of the rectangular piece of land are \[500{\rm{\,m}}\] and \[300{\rm{\,m}}\] respectively. Find its area and the cost of the land if \[1{{\rm{\,m}}^2}\] of the land costs \[{\rm{Rs\,}}10,000\]

Answer 1

Hint: Here, we will use the formula of area of the rectangle and then substitute the given length and breadth in the formula to find the required area of the rectangular piece of land Finally multiplying that area by the cost of \[1{{\rm{\,m}}^2}\] of the land, we will be able to find the required cost of the rectangular piece of land along with its area.
Formula Used:
Area of a rectangle, \[A = l \times b\], where \[l\] is the length and \[b\] is the breadth of the rectangle.

Complete step-by-step answer:
According to the question, we are given that,
Length of the rectangular piece of land, \[l = 500{\rm{\,m}}\]
Breadth of the rectangular piece of land, \[b = 300{\rm{\,m}}\]
The area of the rectangular piece of land is given by the formula \[A = l \times b\]. Therefore,
Area of this rectangular piece of land \[ = l \times b\]
Substituting the values of length and breadth in the above equation, we get
\[ \Rightarrow \] Area of this rectangular piece of land \[ = 500 \times 300\]
Multiplying the terms, we get
\[ \Rightarrow \] Area of this rectangular piece of land \[ = 1,50,000{{\rm{m}}^2}\]
Thus, the area of the given rectangular piece of land is \[1,50,000{{\rm{m}}^2}\]
Now, it is given that,
The cost of \[1{{\rm{m}}^2}\] of the land \[ = {\rm{Rs}}10,000\]
Thus, by using unitary method,
The cost of \[1,50,000{{\rm{m}}^2}\] of the land \[ = 10,000 \times 1,50,000\]
Multiplying the terms, we get
\[ \Rightarrow \] The cost of \[1,50,000{{\rm{m}}^2}\] of the land \[ = {\rm{Rs}}1,50,00,00,000\]
Hence, the required area of the rectangular piece of land is \[1,50,000{{\rm{m}}^2}\] and its cost is \[{\rm{Rs}}1,50,00,00,000\].
Thus, this is the required answer.

Note: A rectangle is a two-dimensional shape having four sides and four angles. Since all the four angles of a rectangle are right angles, hence, it is also known as an equiangular quadrilateral. This is because the rectangle is a type of quadrilateral having all four angles as \[90^\circ \]. In this question, the unitary method helped us to find the cost of the rectangular piece of land. According to this method, after knowing the value of a single unit, we simply multiply both the sides of the required unit by that single unit.