Explanation:
the area of a triangle is
baseline × height / 2
20 = (x-8)×2x/2
40 = (x-8)×2x
20 = (x - 8) × x = x² - 8x
x² - 8x - 20 = 0
the solution to such a square equation is defined
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 1
b = -8
c = -20
x = (8 ± sqrt(64 - 4×-20))/2 = (8 ± sqrt(64+80))/2 =
= (8 ± sqrt(144))/2 = (8 ± 12)/2 = 4 ± 6
x1 = 4 + 6 = 10
x2 = 4 - 6 = -2
but a negative x would also create a negative base length and negative height, so this is not valid for our problem.
that leaves us with x = 10
a base length of x-8 = 10-8 = 2 cm
and a height of 2x = 2×10 = 20 cm