Question

If the length and breadth of a rectangle are doubled than its perimeter is
a). Tripled
b). Doubled
c). Made half
d). None of these

Answer 1

Hint: For the type of question when no value is given and we need to find some relation or value then assume them. For example here as no value of length and breadth are given then assume the length be ‘l’ and breadth be ‘b’. As this will help us to solve in a simpler way. Now move forward according to the question, where you will get the result irrespective of the variable you have chosen. So in our question

Complete step-by-step solution:
Let length be equal to $'l'$
And breadth be equal to $'b'$
Since the question talks about perimeter so as we know that the
Perimeter of rectangle $=~2\left( l+b \right)$ \[equation\text{ }\left( i \right)\]
Now according to the question we want to know, what will be the perimeter if the length and breadth of the rectangle will increase by two, or will it double? So new parameters of rectangle when its length and breadth will get double on initial one
Double length of rectangle of initial one$=~2\times l=2l$
Double breadth of rectangle of initial one $=~2\times b=2b$
So the perimeter of new rectangle whose length and breadth are double of initial one are:
As we know that
Perimeter of rectangle $=~2\left( l+b \right)$
Where $'l'$ is the length of double length of rectangle and $'b'$ is the breadth of double breadth rectangle
So,
Perimeter of new rectangle$=~2\left( 2l+2b \right),~$ (by taking 2 common)
Perimeter of new rectangle $=~2\times 2\left( l+b \right)$ equation (ii)
As from equation (i) perimeter of initial rectangle is $=~2\left( l+b \right)$
So from equation (i) and (ii)
Perimeter of new rectangle$=~2\times 2\left( l+b \right)$
$\text{Perimeter of new rectangle}=\text{ }\!\!~\!\!\text{ }2\times \text{perimeter of initial rectangle}$
Hence, the perimeter will be double of if we double the length and breadth of rectangle
So doubled is the answer.

Note: Always when there is no value is given and we need to find out the relation between area, perimeter or in volume you can assume the parameters of a shape and can solve it. At last you will get the answer in terms of assumed variables you had assumed, so in last put the value of these assumed variables as we did in the last equations in this example.