the height of a triangle is 4 feet greater than 4 times its base. if the area of the triengle is 84ft^2, what is the height of the triangle?

Given: Area of triangle = 84 square feet

height = 4 feet greater than 4 times its base

h=4b + 4

Area of triangle = 1/2 (b) (h)

plugging for area and height

84=1/2 (b) * (4b+4)

168=4b² + 4b

4b²+4b-168=0

taking out 4 common as gcf

b²+b-42=0

factorising we get

(b+7) (b-6) = 0

b=6, - 7

since length cannot be negative so base = 6feet

height = 4b+4 = 24+4=28 feet