The breadth of a rectangle is two third of its length if the perimeter is 30 m find the length and the breadth of a rectangle

Question

The breadth of a rectangle is two third of its length if the perimeter is 30 m find the length and the breadth of a rectangle

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Ayla 1 week 2021-11-22T00:29:58+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-22T00:31:15+00:00

    Answer:

    Let the length of the rectangle be “L”.

    Given:

    Breadth of the rectangle = two – third of length.

    Breadth = 2L/3

    And it’s Perimeter = 30 m

    We know that,

    Perimeter of a rectangle = 2(Length + Breadth)

    \sf  →2(L+  \frac{2L}{3} ) = 30 \: m \\  \\ \sf{→2( \frac{3l + 2l}{3} ) = 30} \\  \\\sf{→ 6L + 4L = 30(3) }\\  \\\sf{→ 10L = 90} \\  \\\sf{→ L =  \frac{90}{10} } \\  \\ \sf{→L = 9 \: m } \\  \\ \sf{Breadth \:  =  \frac{2L}{3} } \\  \\\sf{→ Breadth =  \frac{2(9)}{3}}  \\  \\ \sf{→Breadth \:  = 6 \: m}

    Hence, the dimensions of the rectangle are 9 m and 6 m.

    0
    2021-11-22T00:31:33+00:00

    Length = 9 m

    Breadth = 6 m

    Step-by-step explanation:

    Given:

    • Breadth of rectangle is two third of its length.
    • Perimeter of the rectangle is 30 m.

    To Find:

    • What is the measure of length & breadth of rectangle ?

    Solution: Let the length of rectangle be L m.

    ∴ Breadth = 2/3 of Length

    Breadth = 2/3 \times L

    Breadth = 2L/3 m.

    As we know that –

    Perimeter of rectangle = 2 ( Length + Breadth )

    But, A/q

    • Perimeter = 30 m.

    \implies{\rm } 30 = 2 ( Length + Breadth )

    \implies{\rm } 30 = 2 ( L + 2L/3 ) {Take LCM }

    \implies{\rm } 30 = 2 ( 3L + 2L/3 )

    \implies{\rm } 30 = 2 \times 5L/3

    \implies{\rm } 30 = 10L/3

    \implies{\rm } 30 \times 3 = 10L

    \implies{\rm } 90 = 10L

    \implies{\rm } 90/10 = L

    \implies{\rm } 9 m = L

    Hence, the Length of rectangle is L = 9 m.

    ∴ Breadth of rectangle = 2L/3

    ➟ 2 \times 9/3

    ➟ 18/3 = 6 m.

    _______________________

    ★ Verification ★

    30 m = 2 ( L + B ) m

    30 m = 2 ( 9 + 6 ) m

    30 m = 2 (15) m

    30 m = 30 m

    [ Verified ]

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