Question

The perimeter of a rectangle is 26cm. If its length is 3cm more than its breadth, find the dimensions of the rectangle.

Answer 1

Hint:
We will use the formula of perimeter of the rectangle: $2\left( {l + b} \right)$ , where l is the length of the rectangle and b is the breadth of the rectangle. We will write the length of the rectangle in terms of the breadth of the rectangle and then put their value in the formula of the perimeter.

Complete step by step solution:
We are given the perimeter of the rectangle as 26cm.
It is also stated that the length of the rectangle is 3cm more than the breadth of the rectangle.

Let ABCD be the rectangle and its breadth BC be x cm. Therefore, the length of the rectangle of the rectangle will be $AB = x + 3$ cm.
Putting the value of the length and the breadth of the rectangle in the formula of the perimeter of the rectangle = $2\left( {l + b} \right)$, where l is the length and b is the breadth of the rectangle, we get
$ \Rightarrow $ Perimeter of ABCD = $2\left( {l + b} \right)$
$ \Rightarrow $ Perimeter of ABCD =$2\left[ {\left( {x + 3} \right) + x} \right]$
$ \Rightarrow $ Perimeter of ABCD =$2\left[ {2x + 3} \right]$
$ \Rightarrow $ Perimeter of ABCD =$4x + 6$
Putting the given value of the perimeter of ABCD, we get
$ \Rightarrow $ Perimeter of ABCD = 26 =$4x + 6$
$
   \Rightarrow 4x = 32 \\
   \Rightarrow x = \dfrac{{32}}{4} = 8 \\
 $
Therefore, the breadth of the rectangle is x = 8cm.

Hence, the length of the rectangle is x + 3 = 11cm.
So, the dimensions of the rectangle are $\left( {8 \times 11} \right){\text{cm}}$.

Note:
Such questions can be solved directly by implementing the formulae of the basic geometry shapes such as we used the formula of the perimeter which can either be memorized or you can calculate using the definition of the perimeter as: perimeter is defined as the total measure of the boundary of any shape (2 – D). You need to be careful while deducing the equation of dimensions of the rectangle from the given word problem.