The width of a rectangle is three fourth the length. If the perimeter is 84 cm , find the length and width of the rectangle ?

Hint: With the given condition we get that $w = \dfrac{3}{4}l$and we are given that the perimeter of the rectangle is 84 cm and we know that the formula of perimeter of a rectangle is $Perimeter = 2\left( {l + w} \right)units$ and using the value of w and equating with the given perimeter we get the value of l and using that we can find the value of w.

Complete step-by-step answer:
We are given a condition that the width of the rectangle is three fourths its length
That is $w = \dfrac{3}{4}l$ ………(1)
We are given that the perimeter of the rectangle is 84 cm
We know that the perimeter of the rectangle is given by the formula
$ \Rightarrow Perimeter = 2\left( {l + w} \right)units$
Using (1) and the given perimeter in the above formula
$
   \Rightarrow 84 = 2\left( {l + \dfrac{3}{4}l} \right) \\
   \Rightarrow 84 = 2\left( {\dfrac{{4l + 3l}}{4}} \right) \\
   \Rightarrow 84 = \left( {\dfrac{{7l}}{2}} \right) \\
   \Rightarrow 84*2 = 7l \\
   \Rightarrow \dfrac{{84*2}}{7} = l \\
   \Rightarrow 12*2 = l \\
   \Rightarrow 24 = l \\
$
Hence we get the length of the rectangle to be 24 cm
Using this in (1) we can get the value of w
$
   \Rightarrow w = \dfrac{3}{4}*24 \\
   \Rightarrow w = 3*6 \\
   \Rightarrow w = 18cm \\
$
Hence we get the width of the rectangle to be 18 cm
Hence the length and width of the rectangle is 24 cm and 18 cm respectively.

Note: There are instances when a student may forget the perimeter formula.
Instead of the formula we can find the perimeter by adding the sides of the rectangle