Question

The area of a rectangular plot is \[528{{m}^{2}}\]. The length of the plot is one more than twice its breadth. We need to find the length and breadth of the plot

Answer 1

Hint: This type of question is based on the concept of areas of figures. We can solve this question with the help of the formula of the area of the rectangle that is \[l\cdot b\], where \[l\] is the length and \[b\] is the breadth of the rectangle. From this question we have, Area of the rectangular field = \[528{{m}^{2}}\]. We will find \[l\] and \[b\] by taking \[l=\] \[\left( 2b+1 \right)\] as given. The Area can be found out by multiplying the length of the rectangle with the breadth of the rectangle.

Complete step-by-step solution:
Given,
Area = 528 square metres
Length = (2b+1) metres
So, we can write,
\[Area\]\[=l\cdot b\]
Substituting the length as \[l=\left( 2b+1 \right)\] in the above formula of area of the rectangle, we get,

\[\Rightarrow \]\[528=\left( 2b+1 \right)\cdot b\]
\[\Rightarrow \]\[0=2{{b}^{2}}+b-528\]
\[\Rightarrow \]\[0=\left( b-16 \right)\left( 2b+33 \right)\]
\[\Rightarrow \]\[b=16\] or \[b=-\dfrac{33}{2}\]
Since the value of \[b\] cannot be negative,
\[\therefore \] \[b=16m\]
Hence, we have got the value of the breadth of the rectangular field \[16\]m. Now, we need to find the length of the rectangular field.
So,
\[\begin{align}
  & 528=l\cdot b \\
 & 528=l\cdot 16 \\
 & \therefore \,\,l=33m \\
\end{align}\]
Hence, the length of the rectangular field is \[33\]m.

Note: While solving this question, the students may make a mistake by taking the breadth as negative but that is not possible since the dimension cannot be negative and hence, we need to eliminate the negative value of \[b\].