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20 July, 09:35

A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle?

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  1. 20 July, 09:39
    0
    The equation can be formatted as (w-1) (l+4) = 60

    There are many ways to solve this but I decided to just plug in numbers.

    I established w is 7 and L was 6 initially.

    The long way to solve this would be by completing the square which is literally impossible to diagram on this website.
  2. 20 July, 09:52
    0
    Let the Width of the Original Rectangle be : W

    Given : Length of the Original Rectangle is 4 times as long as it's Width

    ⇒ Length of the Original Rectangle = 4 * W = 4W

    Now Some Modifications are made, So that Original Rectangle becomes into a New Rectangle.

    Given the Length of New Rectangle is 4 inches More than Length of Original Rectangle.

    ⇒ Length of New Rectangle = 4W + 4

    Given the Width of New Rectangle is One Inch less than Width of Original Rectangle.

    ⇒ Width of New Rectangle = W - 1

    We know that Area of a Rectangle is : Length * Width

    Given the Area of New Rectangle is 60 inches²

    ⇒ (4W + 4) (W - 1) = 60

    ⇒ 4W² - 4W + 4W - 4 = 60

    ⇒ 4W² - 4 = 60

    ⇒ 4W² = 64

    ⇒ W² = 16

    ⇒ W = 4

    Dimensions of Original Rectangle:

    Length of Original Rectangle = 4W = 4 * 4 = 16 inches

    Width of Original Rectangle = W = 4 inches
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