Question

The width of the rectangle is two third of its length. If the perimeter is 180m then the dimensions of rectangle are:
(a) The length of the rectangle is 64m and the breadth of is 27m.
(b) The length of the rectangle is 24m and the breadth of is 16m.
(c) The length of the rectangle is 54m and the breadth of is 36m.
(d) The length of the rectangle is 34m and the breadth of is 24m.

Answer 1

Hint: We solve this problem by using the simple formula of perimeter of a rectangle. Let us take a rectangle ABCD as follows:

The perimeter of a rectangle is given as
 \[p=2\left( l+b \right)\]
Where, \['l'\] is the length of the rectangle and \['b'\] is the breadth of the rectangle.
By using this formula and the given condition we find the dimensions of the rectangle.

Complete step-by-step answer:
Let us assume that the length of the rectangle as \['l'\] and the breadth of the rectangle as \['b'\]
We are given that the width of rectangle is two third of its length
We know that the width and breadth both are the same.
Now, by converting the given statement into mathematical equation we get
 \[\Rightarrow b=\dfrac{2}{3}l.....equation(i)\]
We are given that the perimeter of the rectangle is 180m.
Let us assume that the given perimeter as
 \[\Rightarrow p=180m\]
We know that the formula for perimeter of a rectangle is given as
 \[p=2\left( l+b \right)\]
Where, \['l'\] is the length of the rectangle and \['b'\] is the breadth of the rectangle.
Now, by using this formula to given rectangle we get
 \[\begin{align}
  & \Rightarrow 180=2\left( l+b \right) \\
 & \Rightarrow l+b=90 \\
\end{align}\]
Now, by substituting the value of \['b'\] from equation (i) in above equation we get
 \[\begin{align}
  & \Rightarrow l+\dfrac{2}{3}l=90 \\
 & \Rightarrow \dfrac{5}{3}l=90 \\
\end{align}\]
Now, by cross multiplying the terms from LHS to RHS we get
 \[\begin{align}
  & \Rightarrow l=90\times \dfrac{3}{5} \\
 & \Rightarrow l=54m \\
\end{align}\]
Now, by substituting the value of \['l'\] in equation (i) we get
 \[\begin{align}
  & \Rightarrow b=\dfrac{2}{3}\times 54 \\
 & \Rightarrow b=36m \\
\end{align}\]
Therefore, the length of rectangle is 54m and the breadth of rectangle is 36m

So, the correct answer is “Option C”.

Note: Sometimes they may ask the continuation of this problem to find the area of the rectangle.
The formula of area of rectangle is given as
 \[\Rightarrow A=l\times b\]

By substituting the value of length and breadth in above formula we get
 \[\begin{align}
  & \Rightarrow A=\left( 54m \right)\times \left( 36m \right) \\
 & \Rightarrow A=1944{{m}^{2}} \\
\end{align}\]
Therefore the area of given rectangle is \[1944{{m}^{2}}\]
This may be the optional question or may be the continuous answer for the given question.
Students need to remember this area formula also.