Given:
Area = 56
Let l be the length and w be the width.
l = 3w + 2
But we know that;
Area = l x w
Substitute for area and length
56 = (3w+2) x w
Open the parenthesis
56 = 3w² + 2w
Re-arrange:
3w² + 2w - 56 = 0
We can now solve the above quadratic equation using factorisation method
Multiply 3 by -56, this gives - 168
So we find two numbers whose product gives -168 and sum gives 2
The two numbers are 14 and -12
Replace the coefficient of 2 by these two numbers.
3w² + 14w - 12w - 56 = 0
w(3w + 14) - 4( 3w + 14) = 0
(w-4)(3w+14) = 0
Either w - 4 = 0 or 3w + 14 = 0
Either w = 4 or w = -14/3
There is no negative dimension, so we will only pick the positive value.
Therefore, w = 4
Substitute w in l = 3w + 2
l = 3(4) + 2 = 12 + 2 = 14
Therefore,
The length = 14 cm and the width = 4 cm