Answer:
See below.
Step-by-step explanation:
The area of the smaller rectangle = x(x - 4)
The area of the larger one = 3x(x - 2).
So we have
x(x - 4) + 3x(x - 2) = 36
x^2 - 4x + 3x^2 - 6x - 36 = 0
4x^2 - 10x - 36 = 0
Dividing through by 2:
2x^2 - 5x - 18 = 0 <-------- as required.
Solving for x:
2x^2 - 5x - 18 = 0
(2x - 9)(x + 2 ) = 0
2x = 9 or x + 2 = 0
x = 4.5 (we ignore the other result, x = -2).
So AB = 4.5 cm Answer.
