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:
Formula for calculating area of a rectangle of dimension l, b is \[area=l\times b\]and formula for calculating perimeter of a rectangle of dimension l, b is \[perimeter=2\times (l+b)\]. Difference between length and breadth can be represented as\[l-b\].

Complete step by step solution:
Let \[l\]and \[b\]be the length and breadth of a rectangle and perimeter of a rectangle is 206m and formula to find perimeter of rectangle is:
\[\Rightarrow perimeter=2\times (l+b)=206m\]
The formula to find area of rectangle is:
\[\Rightarrow area=l\times b\]
Given that difference between the length and breadth of a rectangle is 23m that is
 \[\Rightarrow l-b=23m\]
Equations are
\[
   \Rightarrow perimeter=2(l+b)=206(1) \\
  \Rightarrow l-b=23(2) \\
\]
Solve equation (2) and find value of l in terms of b
\[
   \Rightarrow l-b=23 \\
  \Rightarrow l=23+b \\
\]
Substitute the value of l in equation (1)
\[
   \Rightarrow 2(l+b)=206 \\
  \Rightarrow l+b=206\div 2 \\
  \Rightarrow l+b=103 \\
  \Rightarrow 23+b+b=103 \\
  \Rightarrow 23+2b=103 \\
\]
Solving the equation
\[
   \Rightarrow 2b=103-23 \\
  \Rightarrow 2b=80 \\
  \Rightarrow b=80\div 2 \\
  \Rightarrow b=40m \\
\]
Substitute the value of b in equation (1)
 \[
   \Rightarrow l-b=23 \\
  \Rightarrow l-40=23 \\
  \Rightarrow l=40+23 \\
  \Rightarrow l=63m \\
\]
Therefore, length of rectangle is 63m and breadth of rectangle is 40m
Area of rectangle is calculated by substituting the values of length and breadth in the given formula:
\[
   \Rightarrow area=l\times b \\
  \Rightarrow area=63\times 40 \\
  \Rightarrow area=2520{{m}^{2}} \\
\]

Therefore, the area of rectangle is (B) 2520$m^2$

Note:
Find the value of l in terms of b and substitute the term l in formula for perimeter. Breadth of rectangle can be found using the formula for perimeter and substitute the value of breadth in equation (1) and find the value of length. Substitute the values of length and breadth in formula for area of rectangle.