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.