The breadth of a rectangle is 3 less than the length. If both the length and the breadth are reduced by 3 units, the area of the rectangle r

Question

The breadth of a rectangle is 3 less than the length. If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90sq. units. Find the dimensions of the original rectangle and also the area.

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Eva 1 month 2021-08-18T05:40:45+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-18T05:41:45+00:00

    Answer

    Length of the rectangle = 18 cm

    Breadth of the rectangle = 15 cm

    Area of the rectangle = 270 cm²

    Given

    The breadth of a rectangle is 3 less than the length. If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90 sq. units.

    To Find

    Dimensions of original rectangle

    Area of the rectangle

    Point to be noted

    Area of rectangle = Length × Breadth

    ⇒ A = lb

    Solution

    Let the length of the rectangle be , ” x

    Breadth be , ” y

    A/c , ” The breadth of a rectangle is 3 less than the length

    ⇒ y = x – 3

    x – y = 3 … (1)

    Area of the rectangle = xy

    A/c , ” If both the length and the breadth are reduced by 3 units, the area of the rectangle reduces by 90 sq. units

    ⇒ ( x – 3 )( y – 3 ) = xy – 90

    ⇒ xy – 3x – 3y + 9 = xy – 90

    ⇒ 3x + 3y = 99

    x + y = 33 … (2)

    Solve (1) + (2) ,

    ⇒ ( x – y ) + ( x + y ) = 3 + 33

    ⇒ x – y + x + y = 36

    ⇒ 2x = 36

    x = 18 cm

    On sub. x value in (1) , we get ,

    ⇒ (18) – y = 3

    ⇒ y = 18 – 3

    y = 15 cm

    So , Area of the rectangle = xy = 270 cm²

    0
    2021-08-18T05:42:05+00:00

    Answer:

    l = 18 units, b = 15 units

    Step-by-step explanation:

    Let the length be l, and breadth be b.

    Given, b = l – 3

    So, area = lb = l(l-3) = l^2 – 3l

    When length and breadth are reduced by 3 units, then new length and breadth = (l-3) and (b-3) or (l-6) units.

    Given, (l-3)(l-6) =  l^2 – 3l – 90

               l^2 – 9l + 18 = l^2 – 3l – 90

               6l = 108

               l = 18 units.

               b = l – 3 = 18 – 3 = 15 units

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