Question

How to find dimensions of a rectangle with a perimeter of \[24\]m?

Answer 1

Hint: We define rectangle as a special parallelogram . Rectangle has some special properties. A rectangle is a quadrilateral in which opposite sides are equal and all four angles are equal with each of its four angles is a right angle. A rectangle has two diagonals and both the diagonals bisect each other. We define the perimeter of a two-dimensional figure as the total length of all the sides which bind the figure. We have different formulas for finding the perimeter of different figures.

Complete step by step solution:
The perimeter of the given rectangle is \[24\]m.
We don't know anything about the dimensions of the rectangle, so we assume the length and breadth of the rectangle to be some variation.
Let the length of the rectangle be $l$.
Let the breadth of the rectangle be $b$.
According to the formula for the perimeter of a rectangle ,
\[Perimeter=2\left( length+breadth \right)\]
We can put the values in the formula to get
\[24=2\left( l+b \right)\]
On solving this equation , we get
\[\begin{array}{*{35}{l}}
   l+b=24/2 \\
   l+b=12 \\
   b=12-l \\
\end{array}\]

Hence we get the dimensions of the rectangle as
Length is $l$m
And breadth is $(12-l)$m.

Note:
We can find the value of length and breadth as constants if we are given the value of either the length or the breadth of the rectangle. We can also find the value of length and breadth if we are given the area of the rectangle. Then it will become a linear equation in two variables and we can solve both the equations to get the dimensions of the rectangle. We should also note that the formula for finding the perimeter is different for different categories of figures.