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30 April, 02:40

When measuring the length a and the width b of a rectangle, it was found that 5.4< a< 5.5 and 3.6< b< 3.7 (in centimeters). Find the possible values of: the perimeter of the rectangle

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  1. 30 April, 04:40
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    The possible values of the perimeter of the rectangle is between 18 and

    18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - The perimeter of any quadrilateral is the sum of the length of its

    four sides

    - The rectangle is a quadrilateral with each two opposite sides are

    equal in lengths, then its perimeter = 2l + 2w, where l, w are its

    length and width

    ∵ The the length of the rectangle is a

    ∵ 5.4 < a < 5.5 cm

    ∵ The perimeter of the rectangle = 2a + 2b

    - Lets multiply the inequality by 2

    ∴ 5.4 * 2 < a * 2 < 5.5 * 2

    ∴ 10.8 < 2a < 11 ⇒ (1)

    ∵ The width of the rectangle is b

    ∵ 3.6 < b < 3.7 cm

    - Lets multiply the inequality by 2

    ∴ 3.6 * 2 < b * 2 < 3.7 * 2

    ∴ 7.2 < 2b < 7.4 ⇒ (2)

    - Add inequalities (1) and (2)

    ∵ 10.8 < 2a < 11

    + 7.2 < 2b < 7.4

    ∴ 18 < 2a + 2b < 18.4

    ∵ 2a + 2b represents the perimeter of the rectangle

    ∴ The possible values of the perimeter of the rectangle is between

    18 and 18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm
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