Question

The perimeter of a rectangle is 12 m . The length is 3 more than twice its width. What is the value of length and width in m?
a.3 , 2
b.3, 3
c.5 , 1
d.4 , 2

Answer 1

Hint: With the given condition we get that $l = 3 + 2w$ and we are given that the perimeter of the rectangle is 12 m and we know that the formula of perimeter of a rectangle is $Perimeter = 2\left( {l + w} \right)units$ and using the value of l and equating with the given perimeter we get the value of w and using that we can find the value of l.

Complete step-by-step answer:
We are given a condition that the length of the rectangle is three more than twice its width
That is $l = 3 + 2w$ ………(1)
We are given that the perimeter of the rectangle is 12 m
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
\[
   \Rightarrow 12 = 2\left( {3 + 2w + w} \right) \\
   \Rightarrow 12 = 2\left( {3 + 3w} \right) \\
   \Rightarrow 12 = 6 + 6w \\
   \Rightarrow 12 - 6 = 6w \\
   \Rightarrow 6 = 6w \\
   \Rightarrow \dfrac{6}{6} = w \\
   \Rightarrow 1 = w \\
\]
Hence we get the width of the rectangle to be 1 m
Using this in (1) we can get the value of l
$
   \Rightarrow l = 3 + 2w \\
   \Rightarrow l = 3 + 2\left( 1 \right) \\
   \Rightarrow l = 3 + 2 = 5m \\
$
Hence we get the length of the rectangle to be 5 m
Hence the length and width of the rectangle is 5 m and 1 m respectively
Therefore the correct option is c.

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