the length of a rectangle is 4 meters less than twice its width. The area of the rectangle is 70. Find the dimensions of the rectangle

Question

the length of a rectangle is 4 meters less than twice its width. The area of the rectangle is 70. Find the dimensions of the rectangle

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Eirian 5 years 2021-09-03T00:14:07+00:00 1 Answers 735 views 1

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  1. Nick
    1
    2021-09-03T00:15:33+00:00
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    Answer:  The width is 7 meters. The length is 10 meters.

    Step-by-step explanation:   Area = Length × width

    Length is 2w – 4  

    Substitute that value for length, then solve for w.

    70 = w(2w – 4)

    70 = 2w² – 4w  reorganize to quadratic equation form

    2w² – 4w -70 = 0   These are All even numbers; factor out 2 (divide all by 2)

    w² – 2w – 35 = 0  factor this

    (w – 7)(w + 5)    set each factor = 0 and calculate the value of w.

    w+5=0  w= -5  (disregard this one because dimensions of real rectangles can’t be negative)

    w – 7 = 0  w = 7   The width is 7

    Substitute into the original expressions to get the value of Length.

    2(7) -4 = L    14 – 4 = L  The Length is 10.

    Check by substituting into the original equation:

    w × 2w -4 = 70

    7 × 2(7) -4 = 70

    7 × 10 = 70    TRUE!

    w

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