Question

Find the length and breadth of the rectangle given below if its perimeter is $ 72m. $

Answer 1

Hint: Perimeter of rectangle is the sum of all the four sides. Here, we will convert the given word statement in the mathematical expression. By the given known terms and the correlation will find the unknown length and breadth.

Complete step-by-step answer:
Given that:
Length of the rectangle $ l = 5x + 4 $
Breadth of the rectangle $ b = x - 4 $
We know that –
Perimeter of the rectangle $ = 2(l + b) $
Now, place the given perimeter is $ 72 $ m and also the given length and breadth relation in the above equation –
 $ 72 = 2(5x + 4 + x - 4) $
Now, simplify the above equation and make the unknown “x” the subject –
 $
  72 = 2(6x) \\
  72 = 12x \\
  $
When the number in multiplicative at one side changes its side goes to the numerator-
 $
   \Rightarrow x = \dfrac{{72}}{{12}} \\
   \Rightarrow x = 6 \\
  $
Now, the required length, $ l = 5x + 4 $
Place the value of “x” in the above equation and simplify.
Length, $ l = 5(6) + 4 $
Length, $ l = 34m{\text{ }}....{\text{ (a)}} $

Now, the required breadth, $ b = x - 4 $
Place the value of “x” in the above equation and simplify.
Breadth, $ b = 6 - 4 $
Breadth, $ l = 2m{\text{ }}....{\text{ (b)}} $
Hence, the required answer - the length of the rectangle is $ 34m $ and the breadth of the rectangle is $ 2m $ .

Note: Rectangle can also be defined as the parallelogram containing right angles. A rectangle with four equal sides is a square. Do not forget to write the units in the length and breadth resultant answer.
The word “rectangle” was derived from the latin language “rectangulus” which is the combination of rectus. It is the parallelogram with equal diagonals and is also known as equiangular quadrilateral.