Question 165441
Let:
triangle's base = b
triangle's height = h

b = 2h - 6


triangle's area = 54
<=>{{{(1/2)*b*h = 54}}}
<=>{{{(1/2)*(2h - 6)*h = 54}}}
<=>{{{(1/2)*(2h^2 - 6h) = 54}}}
<=>{{{h^2 - 3h = 54}}}
<=>{{{h^2 - 3h - 54 = 0}}}
use factorization, we will get:
(h - 9)*(h + 6) = 0
h - 9 = 0
h = 9
or
h + 6 = 0
h = -6 -> this is not a possible measure for h, because it's negative


so the value of triangle's height = 9 ft
and triangle's base = 2*9 - 6 = 18 - 6 = 12 ft