and CosQ
38. Half the perimeter of a rectangular garden whose length is 4 m more than its
width is 36 m find the dimension of the garden
on method andhan find the
Answers
Appropriate Question :
Half the perimeter of a rectangular garden whose length is 4 m more than its width, is 36 m find the dimension of the garden.
Answer :
Dimensions of the rectangular garden :-
- Length = 20 m
- Breadth = 16 m
Given :
• Half the perimeter of a rectangular garden = 36 m
• Length of the rectangular garden is 4 m more than than its width
To find :
• Dimensions of the garden
Knowledge Required :
Formula to calculate semi perimeter of rectangle :-
⠀⠀⠀⇒ Semi perimeter of rectangle = 2(l + b) ÷ 2
where,
• l denotes the length of the rectangle
• b denotes the breadth of the rectangle
Solution :
Let the breadth of the rectangle be x metre and the length be 4 m more than the breadth, i.e. x + 4 metre
Now, according to the question :
⠀⠀⠀⇒ Semi perimeter of the rectangular garden = l + b
⠀⠀⠀⇒ 36 = x + x + 4
⠀⠀⠀⇒ 36 = 2x + 4
⠀⠀⠀⇒ Transposing 4 to the left hand side and changing it's sign :
⠀⠀⠀⇒ 36 - 4 = 2x
⠀⠀⠀⇒ 32 = 2x
⠀⠀⠀⇒ Transposing 2 to the left hand side :
⠀⠀⠀⇒ 32/2 = x
⠀⠀⠀⇒ 16 = x
The value of x = 16
Substitute the value of x in the dimensions of the rectangular garden :
Length of the rectanglular garden :-
⠀⠀⠀⇒ Length = x + 4
⠀⠀⠀⇒ Length = 16 + 4
⠀⠀⠀⇒ Length = 20
Length of the rectangular garden = 20 m
Breadth of the rectangular garden :-
⠀⠀⠀⇒ Breadth = x
⠀⠀⠀⇒ Breadth = 16
Breadth of the rectangular garden = 16 m
Therefore, the length and breadth of the rectangular garden are 20 m and 16 m respectively.
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VERIFICATION :-
To verify the value of dimensions of the rectangular garden, find the semi perimeter of the rectangular garden if it will be equal to 36 m (as mentioned in the question) then the values are right.
⠀⠀⠀⇒ Semi perimeter = l + b
⠀⠀⠀⇒ Semi perimeter = 20 + 16
⠀⠀⠀⇒ Semi perimeter = 36
Semi Perimeter of the rectangular garden = 36 m
Hence, verified.