Area of a triangle

Question

The area of a triangle is 28 cm2 . If the base is two more than 3 times the height, find the length of the base.

Answer 1

A=(1/2)bh = 28 = (1/2)h(2+3h) = h+ (3/2)h^2

3h^2/2 + h -28 = 0

3h^2 + 2h - 56 = 0

h= -2/6 + or - (1/6)sqr(4+12(56)) = - 1/3 + 13/3 = 12/3 = 4

height = 4 cm

base = 56/4 = 14 cm

b=2+3h = 2+3(4) = 14

28 = (1/2)14(4) = 28