Question

The length of a rectangle is 3 times the width. The perimeter is 96 cm. How do you find the width and length?

Answer 1

Hint: A rectangle is a plane figure with four straight lines and four right angles, especially one with unequal adjacent sides. The longer side length is called length (say L) and the shorter side length is called width (say W). The area of the rectangle is \[L\times W\] and the perimeter of the rectangle is \[2(L+W)\].

Complete step by step answer:
As per the given question, we have to find the dimensions of the given rectangle. The perimeter of the given rectangle is given as 96 cm. We are provided with the relation between the length and width of the rectangle, which says that the length of the rectangle is 3 times the width of the rectangle.

Let the length of the rectangle be L and the width of the rectangle be W as shown in the figure below. Also, let the perimeter of the rectangle to be P.
Perimeter of the rectangle, \[P=2.W+2.L\]. -------(1)

From the given information in the question, we are told \[L=3W\] and \[P=96\] cm.
So, we can rewrite the equation (1) as
\[\Rightarrow P=96=2.W+2.L=2.W+2.(3W)\] ------(2)

In equation (2), we have \[2.(3W)\] which is \[(3W)\] multiplied with 2. This is equal to \[(6W)\]. Replacing \[2.(3W)\] with \[(6W)\], we can write equation (2) as
\[\Rightarrow 96=2.W+6W\]
Addition of \[2W\] and \[6W\] gives \[8W\]. Hence, we get
\[\Rightarrow 8W=96\]
So, \[W=\dfrac{96}{8}=12\] cm and \[L=3.12=36\] cm.

\[\, therefore, \] 12 cm and 36 cm are the width and length of the rectangle respectively.

Note:
 To solve such types of problems we have to know the relation between the perimeter of the rectangle with its length and width which is \[P=2.W+2.L\]. While simplifying equations, we should use the PEMDAS rule. We should avoid calculation mistakes to get the correct results.