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:
We are given the perimeter of rectangle, so we use the formula of perimeter of rectangle and form a equation in terms of length and width, also we are given relation between length and width, so we use that and make another equation, using this two equations we solve for the length and width of rectangle.

Complete step by step solution:
Let length and width be l and b.

The perimeter of the rectangle is given by \[2(l + b)\]

As given that perimeter of rectangle is 12 m, so we have
 \[ \Rightarrow 2(l + b) = 12\]

On dividing by 2 we get,
 \[ \Rightarrow l + b = 6\]
On rearranging we get,
 \[ \Rightarrow l = 6 - b\]

According to the given condition given in the question as the length is 3 more times than twice of breadth
So, the we will get
 \[l = 3 + 2b\]

Now we will substitute value of l from above
 \[ \Rightarrow 6 - b = 3 + 2b\]

On rearranging we get,
 \[ \Rightarrow 6 - 3 = 2b - b\]
On adding like terms, we get
 \[ \Rightarrow 3 = 3b\]
On dividing the equation by 3 we get,
 \[ \Rightarrow \dfrac{3}{3} = b\]
Hence, we have
 \[ \Rightarrow b = 1\]
Substituting value of b in \[l = 6 - b\]
We will get
 \[ \Rightarrow l = 6 - 1\]
So, the value of length is
 \[ \Rightarrow l = 5\]

We get length and breadth as 5, 1 respectively.
Hence, Option (C) is the correct option.

Note:
Perimeter of rectangle is the addition of the boundary which has 2 equal length and breadth. Length is the longer sides of the rectangle; breadth is the shorter side of the rectangle. Addition of all four sides is the perimeter of the rectangle.