Question

The difference between the length and breadth of a rectangle is 23 m. if the perimeter is 260m, then the area of the rectangle is ________.
A. 5025.5 ${{\text{m}}^2}$
B. 4092.75 ${{\text{m}}^2}$
C. 2420 ${{\text{m}}^2}$
D. 2500 ${{\text{m}}^2}$

Answer 1

Hint: In this question, first assume the length and breadth of the rectangle be L and B cm respectively then use the formula for finding the area and perimeter of the rectangle. If L & B are the length and breadth of a rectangle respectively.
Then its Area = (${\text{LxB}}$)
& Perimeter = 2(L+B)

Complete step-by-step answer:

First of all we will make the diagram:

AB is the length of the rectangle and AD is the breadth of the rectangle. It is given that AB-AD = 23m and perimeter = 260m.
Let Length of rectangle = L m
       Breadth of rectangle = B m
According to question:
The difference between the length and breadth of a rectangle is 23 m.
So,
$ \Rightarrow $L-B = 23
$ \Rightarrow $L = 23+B ………… (1)

Also it is given:
Perimeter is 260m.
We know that perimeter of rectangle is given by:
Perimeter = 2(L+B)
So, we can write:
$ \Rightarrow $2(L+B)= 260
$ \Rightarrow $ L+B= 130
$ \Rightarrow $ 23+2B= 130 … [Using Eq.- 1]
$ \Rightarrow $ 2B =107
$ \Rightarrow $ ${\text{B = }}\dfrac{{{\text{107}}}}{{\text{2}}}$
$ \Rightarrow $B= 53.5
Now, putting the value of B in equation (1) and we get
$ \Rightarrow $L = 23+B
          = $23 + \dfrac{{107}}{2}$
          = 23 + 53.5
          = 76.5
Now, we have:
Length of rectangle = 76.5 m
Breadth of rectangle = 53.5 m
Area = length $ \times $ breadth = L$ \times $B
         = 76.5 $ \times $53.5 ${{\text{m}}^{\text{2}}}$
         = 4092.75${{\text{m}}^{\text{2}}}$

Hence, the area of the given rectangle = 4092.75 ${{\text{m}}^{\text{2}}}$.

So option B is correct.

Note: You should know that the opposite sides of a rectangle have the same lengths and are parallel. and also, each angle is ${\text{9}}{{\text{0}}^{\text{o}}}$. This will help you in understanding the derivation of the area of the rectangle and perimeter of the rectangle. Once you understand the derivation , the concept of area and perimeter will fit into your mind forever.