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Activity Discussion Math Dimension Word Problem

  • Dimension Word Problem

    Posted by Varun on June 26, 2023 at 11:27 am

    A rectangular garden has a length that is 4 meters longer than its width. If the diagonal of the garden is 10 meters, what are the dimensions of the garden?

    Hanshika replied 6 months, 3 weeks ago 2 Members · 1 Reply
  • 1 Reply
  • Hanshika

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    December 2, 2023 at 12:47 am
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    ::

    Let the width of rectangle be x

    then length according to question is (x+4)

    Since diagonal of rectangle divides the rectangle into two right angled triangle

    So according to Pythagorean theorem

    Diagonal^2= Length^2 + Width^2 ———- (1)

    According to question, Diagonal = 10 m;

    Therefore , putting the values in (1)

    (10)^2=(x+4)^2+x^2

    100 = x^2+8x+16+x^2

    100 = 2x^2+8x+16

    100-16 = 2x^2+8x

    84=2x^2+8x

    dividing both side by 2

    42= x^2+4x

    x^2+4x-42=0

    by the help of quadratic formula

    picture is attached below, from picture value of x=4.73 m

    so x=width= 4.73m

    (x+4) = length= (4.73+4)= 8.73m

    Therefore the dimension of the garden is (8.73*4.73)meters.

    • This reply was modified 6 months, 3 weeks ago by  Hanshika.
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