The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32 cm, then find the area of the rectangle.​

Question

The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32 cm, then find the area of the rectangle.​

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Parker 2 weeks 2021-11-22T02:00:39+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-22T02:01:45+00:00

    Answer:

    55 cm^2

    Step-by-step explanation:

    Given:

    length = l or (3b – 4)  ……….1

    width = b

    Therefore,

    Perimeter = 2(l+b)

    => 32 = 2[(3b – 4)+b]   ………from 1

    => 32 = 2(4b – 4)

    => 32 = 2*4(b – 1)

    => 32 = 8(b – 1)

    => 32/8 = (b – 1)

    => 4 = (b – 1)

    => 4+1 = b

    => b = 5 cm

    Therefore,

    l = (3b – 4)

     =  15 -4

     =  11 cm

    Therefore,

    Area= l*b

    => 11 *5

    =>55 cm^2

    0
    2021-11-22T02:02:10+00:00

    \huge\underline\mathrm{SOLUTION:-}

    AnswEr:

    • The area of the rectangle is 55 square cm.

    Given that:

    • The length of a rectangle is 4 less than 3 times its width.
    • The perimeter of a rectangle is 32 cm.

    Need To Find:

    • The area of the rectangle= ?

    ExPlanation:

    Let x be the breadth of the rectangle.

    Then, its length is (3x – 4).

    Perimeter of the rectangle is 32 cm [Given]

    ➠ 2(l + B) = 32

    Divide each side by 2.

    ➠ l + B = 16

    Substitute (3x – 4) for l and x for B.

    ➠ 3x – 4 + x = 16

    ➠ 4x – 4 = 16

    Add 4 top each side.

    ➠ 4x = 20

    Divide each side by 4.

    ➠ x = 5

    Therefore:

    • Breadth of the rectangle is 5 cm.

    And length of the rectangle is

    ➠ 3(5) – 4

    ➠ 15 – 4

    11 cm

    Formula used here:

    • Area of a rectangle = Length × Breadth

    Substitute 11 for l and 5 for B.

    ➠ 11 × 5

    55

    Hence:

    • The area of the rectangle is 55 square cm.

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    Additional Information:

    What is Perimeter?

    • The length of the boundary of a closed figure is called the perimeter.
    • Perimeter of rectangle = 2 × (Length + Breadth)
    • Perimeter of a square = 4 × Side

    What is Area?

    • The measure of the surface enclosed by a closed figure is called area.
    • Area of rectangle = Length × Breadth
    • Area of a square = Side × Side

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