Question

Find the square meters, the area of rectangle of length \[ = {\rm{12m}}\] and breadth \[ = {\rm{125cm}}\].

Answer 1

Hint: Find a formula for area of rectangle. Now substitute the values of variables you need to solve the equation. By this you will get the value of the area of the rectangle. This area is the required result in the question.

Complete step-by-step answer:
Rectangle: In Euclidean plane geometry, a rectangle is a quadrilateral with 4 right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal. It can also be defined as a parallelogram containing a right angle. It is a two-dimensional shape.
Besides the above definition we can also define the rectangle as a combination of strips of breadth db upto b each of length l.

As you can see if we integrate the area of the strip from \(x = 0\) to \(x = b\)we get the area of the rectangle.
\[Area{\text{ of rectangle = }}\int\limits_0^b {ldb} \]
As l does not depend on b we can bring it out.
\[Area{\text{ of rectangle = l}}\int\limits_0^b {1db} \]
By basic properties of integration, we know the relation as:
\[\int {1dx = x + c} \]
By substituting this, we can write the equation as:
\[Area{\text{ of rectangle = l}}\left( x \right)_0^b\]
By substituting the limits into function, we get the equation:
\[Area{\text{ of rectangle = l}}\left( {b - 0} \right)\]
By simplifying the above equation, we can write it as:
\[Area {\text { of rectangle = lb}}\]
Given conditions in the question, can be written as follows:
The length of rectangle is given by the equation: \[l = 12m\]
The breadth of rectangle is given by the equation: \[b = 125cm\]
Area of rectangle can be found by substituting these:
\[Area = 12m \times 125cm\] . . . . . . . . . . . . . . . . . . . . (1)
We need to convert 12m into cms.
By basic knowledge of measurement we know the relation
\[1m = 100cm{\rm{ }} \Rightarrow {\rm{1cm = 0}}{\rm{.01m}}\]
By multiplying with 125 on both sides, we get the equation
\[125cm = 1.25m\]
By substituting this into equation (1) we can write it as:
\[Area = 12m \times 1.25m\]
By simplifying above we can write it as follows:
\[Area = 15{m^2}\]
The value of area in square meters is \[15{m^2}.\]

Note: Be careful while integrating generally students confuse and write l(dl) where they get a quadratic but that is for square here we write l(db) which leads to polynomial lb. Alternatively you can convert 12m into cm and find the area in \[c{m^2}\] at last divided by 10000 to get value in \[{m^2}\]. Anyways you get the same result.