Question

The length of a rectangle is 7cm more than its breadth. If the perimeter is 62 cm, find the length and breadth.

Answer 1

Hint: To solve this question, we should know the formula related to perimeter of a rectangle. If the length and breadth of a rectangle are given as L and B respectively, then the perimeter of the rectangle is given by the formula Perimeter = 2 \[\times \] (L + B). Let us consider the breadth of the rectangle B = x. We can infer from the question that the length of the rectangle will be L = x + 7. By applying the values of length and breadth in the perimeter equation and equating it to 62 cm, we get the required dimensions of the rectangle.

Complete step-by-step answer:
Let us consider a rectangle, whose Length = L units and Breadth = B units

Perimeter is defined as the total length of the line which acts as a boundary of the plot.
In the above rectangle, we can write that
Perimeter = L + B+ L + B
Perimeter = 2 \[\times \] (L + B)$\to \left( 1 \right)$.
Let us consider that the breadth of the rectangle given in the question be B = x units. It is given that the length is 7 cm more than the breadth. So, we can write that L = x + 7 units. We can infer from the question that the perimeter of the given rectangle is 62 cm.
Substituting the values of L, B and Perimeter in the equation-1, we get
$62=2\times \left( x+7+x \right)$
Dividing with 2 on both sides, we get
$\begin{align}
  & \dfrac{62}{2}=2x+7 \\
 & 31=2x+7 \\
\end{align}$
Subtracting 7 and then dividing with 2 we get
$\begin{align}
  & 2x+7-7=31-7 \\
 & 2x=24 \\
 & x=12 \\
\end{align}$
$\therefore $The breadth B = 12 cm and the length L = 12 + 7 = 19 cm.

Note: There is a chance of calculation mistakes in calculating the values of length and breadth. To avoid those mistakes, we can check whether our results are correct or wrong. Here in the answer, we can see the length is 7 cm more than the breadth which is the first condition in the question. The perimeter of the rectangle with length = 19 cm and breadth = 12 cm is Perimeter = 2 $\times $(19 + 12) = 2 $\times $ 31 = 62 cm which is the same as the condition in the question. So, the answer can be verified.