Area of any triangle = (1/2) x (base) x (height)
You said ...
Area = 20 cm²
Height = (b + 4)
so we can write the area formula like this,
with everything in centimeters:
20 = (1/2) x (b) x (b + 4)
Eliminate the parentheses on the right: 20 = (1/2) (b² + 4b)
Multiply each side by 2 : 40 = b² + 4b
Subtract 40 from each side: b² + 4b - 40 = 0
Use the quadratic formula to solve this equation,
and you find that
b = -2 plus or minus 6.633
b = 4.633
b = -8.633
The meaningful solution is base = 4.633 cm
Check:
Area = (1/2) (b) (b+4) =
(1/2) (4.633) (8.633) =
(1/2) (40 cm²) = 20 cm² yay !