Question

Find the length and breadth of a rectangle given that its perimeter is $240cm$ and the length is $4$ times its breadth.

Answer 1

Hint: In this problem, we need to find out the length and breadth of a rectangle. We are also given two conditions of the corresponding rectangle. At first, we assume the length as “l” cm and the breadth as “b” cm. The two equations formed will be,
$2\left( l+b \right)=240....\left( i \right)$
$l=4b....\left( ii \right)$
Solving them, we get the values of “l” and “b”.

Complete step by step answer:
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
Now, let us assume that the length of the rectangle is “l” cm and the breadth is “b” cm. Then, the perimeter of the rectangle will be $2\left( l+b \right)$ . Now, we are given that the perimeter of this rectangle is equal to $240cm$ . This means that,
$2\left( l+b \right)=240....\left( i \right)$
It is also given that the length of the rectangle is $4$ times its breadth. This means that,
$l=4b....\left( ii \right)$
We now substitute the value of “l” from the second equation into the first equation and get,
$\begin{align}
  & \Rightarrow 2\left( 4b+b \right)=240 \\
 & \Rightarrow b=24cm \\
\end{align}$
The value of “l” will then be,
$l=4\left( 24 \right)=96cm$
Thus, we can conclude that the length of the rectangle is $96cm$ and the breadth of the rectangle is $24cm$ .

Note: This is an easy problem and this one is the easiest approach to the solution. But, the main mistake that students make here is that they take the formula of the perimeter to be $l+b$ which is wrong and should be avoided.