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

X^2+6x+8=0
To write the above in the form of (x-p)^2=q we proceed as follows:
i] Re-write the expression:
x^2+6x=-8
ii] Calculate for the vale of c.
c=(b/2a)²
given that:
b=6, and a=1
thus
c=(6/2*1)^2=9

iii]
Add 9 on both sides of the equation from i
x^2+6x+9=-8+9
simplifying we get:
x^2+6x+9=1
factoring the LHS we get:
(x+3)(x+3)=1
(x+3)²=1
The above is in the form of:
(x-p)²=q
where:
p=3 and q=1