the breadth of a rectangular garden is 1/4 of it’s length. if it’s perimeter is 30 m find its dimensions​

the breadth of a rectangular garden is 1/4 of it’s length. if it’s perimeter is 30 m find its dimensions​

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  1. Answer:

    • Length and Breadth of the rectangular garden are 12 m and 3 m respectively.

    Step-by-step explanation:

    Given that:

    • The breadth of a rectangular garden is 1/4 of its length.
    • The perimeter of the garden is 30 m.

    To Find:

    • The dimensions of the garden.

    Solution:

    Let us assume:

    • The length of the rectangular garden be 4x.

    Then,

    • The breadth of the rectangular garden will be x.

    As we know that:

    Perimeter of a rectangle = 2(length + breadth) units

    Substituting the values,

    [tex]\sf{Perimeter=2(4x+x)}[/tex]

    [tex]\sf{=2\times5x}[/tex]

    [tex]\sf{=10x}[/tex]

    Hence,

    • Perimeter of the rectangular garden = 10x

    But,

    • Perimeter of the rectangular garden = 30 m (given)

    Therefore,

    [tex]\sf{\longmapsto10x=30\;m}[/tex]

    Transposing 10 from LHS to RHS and changing its sign,

    [tex]\sf{\longmapsto x=\dfrac{30\;m}{10}}[/tex]

    Cutting off the zeros,

    [tex]\sf{\longmapsto x=\dfrac{3\!\!\!\not{0}\;m}{1\!\!\!\not{0}}}[/tex]

    [tex]\bf{\longmapsto x=3\;m}[/tex]

    Hence,

    • Value of x = 3 m

    Therefore,

    • Length of the rectangular garden = 4x = (4 × 3) m = 12 m
    • Breadth of the rectangular garden = x = 3 m
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