Question

Perimeter of a rectangle is 3.4m less than 2/5 of the perimeter of a square. If the perimeter of the square is 40 m, find tje lenght and breadth of the rectangle that breadth is 1/3 of the length

Answer 1

$\textbf{Answer}$

$\textbf{Perimeter(Rectangle) = 2(l+b)}$,where l is length and b is breadth.
$\textbf{Perimeter(Square) = 4(side)}$

Suppose the side of a square is S cm
=> Perimeter of square = 4(S) cm
But perimeter of a square is given 40 cm.
=> 4(S) = 40
=> $\textbf{S = 4 cm}$

Suppose the length of a rectangle is L cm.
Since breadth of a rectangle is 1/3 of length,
=> Breadth of a rectangle = 1/3 L cm.

=> Perimeter of rectangle = 2(L + 1/3 L)
=> Perimeter of a rectangle = 8/3 L

$\textbf{According to the question,}$
Since perimeter of a rectangle is 3.4 less than 2/5 of the perimeter of the square,

=> Perimeter of a rectangle = (2/5) (40)
=> 8/3 L = (2/5) 40 - 3.4
=> 8/3 L = 16 - 3.4
=> 8/3 L = 12.6
=> L = (12.6 × 3)/8
=> $\textbf{L = 4.725 cm}$

=> 1/3 L = (4.725) (1/3)
=> $\textbf{1/3 L = 1.575 cm}$

$\textbf{Length of rectangle = 4.725 cm}$
$\textbf{Breadth of rectangle = 1.575 cm}$

$\textbf{Hope My Answer Helped}$
$\textbf{Thanks}$

Answer 2

Perimeter(Rectangle) = 2(l+b),where l is length and b is breadth.
\textbf{Perimeter(Square) = 4(side)}Perimeter(Square) = 4(side) 

Suppose the side of a square is S cm
=> Perimeter of square = 4(S) cm
But perimeter of a square is given 40 cm.
=> 4(S) = 40
=> \textbf{S = 4 cm}S = 4 cm 

Suppose the length of a rectangle is L cm.
Since breadth of a rectangle is 1/3 of length,
=> Breadth of a rectangle = 1/3 L cm.

=> Perimeter of rectangle = 2(L + 1/3 L)
=> Perimeter of a rectangle = 8/3 L

\textbf{According to the question,}According to the question, 
Since perimeter of a rectangle is 3.4 less than 2/5 of the perimeter of the square, 

=> Perimeter of a rectangle = (2/5) (40)
=> 8/3 L = (2/5) 40 - 3.4
=> 8/3 L = 16 - 3.4
=> 8/3 L = 12.6
=> L = (12.6 × 3)/8
=> \textbf{L = 4.725 cm}L = 4.725 cm 

=> 1/3 L = (4.725) (1/3)
=> \textbf{1/3 L = 1.575 cm}1/3 L = 1.575 cm 

\textbf{Length of rectangle = 4.725 cm}Length of rectangle = 4.725 cm 
\textbf{Breadth of rectangle = 1.575 cm}Breadth of rectangle = 1.575 cm