Math test?

The perimeter of a rectangle is 56 cmeter the area of a rectangle is 96 cm² find the dimension of the rectangle

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  • David
    Lv 7
    2 months ago

    The dimensions of the rectangle are: width = 4 cm and length = 24 cm

    Check: 2*(4+24) = 56 cm

    Check: 4*24 = 96 square cm

  • ?
    Lv 7
    2 months ago

    The perimeter of a rectangle is 56 cm. 

    The area of the rectangle is 96 cm².

    Find the dimensions of the rectangle.

    l + w = 56

    lw = 96

    l ≈ 1.77025, w ≈ 54.2298

  • 2l + 2w = 56

    l * w = 96

    2l + 2w = 56

    l + w = 28

    l = 28 - w

    l * w = 96

    (28 - w) * w = 96

    (w - 28) * w = -96

    w^2 - 28w = -96

    w^2 - 2 * 14w + 14^2 = 14^2 - 96

    (w - 14)^2 = 196 - 96

    (w - 14)^2 = 100

    w - 14 = -10 , 10

    w = 4 , 24

    4 cm by 24 cm

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