Question

The figure shows an irregular quadrilateral and the lengths of its individual sides. Which of the following equations best represents the perimeter of the quadrilateral.

A) $4{m^2} + 5$
B) 5m+5
C) $2{m^4} + 5$
D) ${m^4} + 5$

Answer 1

Hint:
Let us first try to understand the meaning of the perimeter of any polygon. It stands for the length of the sum of all the sides of the polygon. Thus, in order to find the perimeter of any given polygon, all you need to do is add all the lengths of the sides. In the question given to us, we have a quadrilateral. All you need to do is add the given lengths to find its perimeter.

Complete step by step solution:
Given to us is a quadrilateral having the length of the sides as m, 2m, m+2 and m+3 and we need to find the perimeter of the quadrilateral. For that all we need to do is add the lengths of all the sides.
Let:
$
  {\text{Length of the 1st side}} = m + 3 \\
  {\text{Length of the 2nd side}} = m \\
  {\text{Length of the 3rd side}} = 2m \\
  {\text{Length of the 4th side}} = m + 2 \\
 $

Add all of them to find the perimeter of the quadrilateral given in the question.
$
  {\text{Perimeter}} = m + 2m + m + 2 + m + 3 \\
   = 5m + 5 \\
 $

Thus, we get the perimeter of the given figure as 5 m + 5. Thus, the correct option is option (b).


Note:
If in any given question, we have the opposite sides of the 4-sided polygon are equal, then the perimeter of that polygon can be calculated using the formula, ${\text{Perimeter}} = 2 \times \left( {{\text{sid}}{{\text{e}}_1} + {\text{sid}}{{\text{e}}_2}} \right)$
And if in any polygon all the 4 sides are equal then,
${\text{Perimeter}} = 4 \times \left( {\text{s}} \right)$, where ‘s’ stands for the side of the polygon.