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31 August, 20:48

The perimeter of a rectangle is 16units and the area is 12 square units. Find the dimensions of the rectangle

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  1. 31 August, 22:42
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    The length is 6 units

    The width is 2 units

    Step-by-step explanation:

    Let the length be x units and;

    Width be y units

    Perimeter is given by (2 * length) + (2 * width)

    2x + 2y = 16 units

    Area is given by length * width

    x * y = 12 units² or xy = 12 units²

    Simultaneous equations formed:

    2x + 2y = 16 ... (i)

    xy = 12 ... (ii)

    From equation (ii) x = 12/y

    Replacing the value of x in equation (i):

    2 (12/y) + 2y = 16

    Dividing by 2 throughout gives;

    12/y + y = 8

    Multiplying by y gives;

    y² - 8y + 12 = 0

    Solving for y using the quadratic formula gives y = 6 or 2.

    If y is 6, from equation (ii) x = 12/6 = 2

    But we want x > y so y should be 2 units.

    There we go!

    y (width) is 2 units and;

    x (length) is 12/2 = 6 units.
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