If a triangle has a area of 42 cm^2 and a base of 8 cm, what is the height? show work pl

hb=10.5cm

Step-by-step explanation:

Area of triangle = 1/2(height x base)

The problem states that base is 8 cm greater than the height; therefore, base-8 = height.

A = 1/2(b*h)

42 = 1/2(b*[b-8])

84=(b^2-8b)

rearrange to

b^2 - 8b -84

factor to

(b+8)(b-14)

Therefore, b = -8 cm which makes no sense and

b = +14 cm

and height = 14-8 = 6

Check:

1/2(b*h) = area

1/2(14*6) = 1/2(84)=42