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

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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step-by-step explanation:

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step-by-step explanation: