and CosQ
38. Half the perimeter of a rectangular garden whose length is 4 m more than its
width is 36 m find the dimensi

By Ella

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​

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Ella

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  1. 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.

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