Answer:
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.
