Question

The difference between the length and breadth of a rectangle is 23m. if the perimeter is 206m then the area is
A.\[1520{m^2}\]
B.\[2520{m^2}\]
C.\[2420{m^2}\]
D.None

Answer 1

Hint: We are given in the question that the difference between the length and breadth is 23m so we will form an equation with the help of this statement. Next, we are given the perimeter so we will directly apply the perimeter formula and find another equation while solving both the equations simultaneously, we will get the values of length and breadth. Hence, in the last, we will apply the formula of the area of the rectangle to evaluate the area of the rectangle.

Complete step-by-step answer:
First, we will let the length be denoted as \[l\] and breadth as \[b\].
Now, we will consider the given statement that the difference between the length and breadth is given by 23m.
So, we get,
\[l - b = 23\]------(1)
Now, as the perimeter is given as 206, so, we will apply the formula of the perimeter of a rectangle and put it equal to 206.
Thus, we get,
\[
   \Rightarrow 2\left( {l + b} \right) = 206 \\
   \Rightarrow l + b = 103 \\
 \]
Hence, the equation is \[l + b = 103\]-------(2)
Now, we will solve both the equations simultaneously using the substitution method, so we will evaluate the value of the length in terms of breadth from equation (1) and substitute it in equation (2).
Thus, we get from equation (1),
\[ \Rightarrow l = 23 + b\]
Now, we will put the value in equation (2),
\[
   \Rightarrow \left( {23 + b} \right) + b = 103 \\
   \Rightarrow 2b = 80 \\
   \Rightarrow b = 40 \\
 \]
Thus, the value of breadth is 40m.
And the value of length is calculated by substituting the value of breadth,
Thus, we get,
\[
   \Rightarrow l = 23 + 40 \\
   \Rightarrow l = 63 \\
 \]
Hence, the value of length is 63m.
Now, we need to calculate the area of the rectangle using the formula \[A = lb\].
Thus, we get,
\[
   \Rightarrow A = 63\left( {40} \right) \\
   \Rightarrow A = 2520 \\
 \]
Hence, the area of the rectangle is given by \[2520{m^2}\]
Thus, option B is correct.
Note: We need to remember the formulas of the area of rectangle and perimeter of the rectangle. We can solve the equations by the elimination method also. It is necessary to form two equations to find the value of length and breadth to evaluate the area of the rectangle. It is important to analyze the given statement properly.