Answer:
height = 12 cm
Step-by-step explanation:
Area of a triangle is given by
[tex]A = \frac{1}{2} bh[/tex]
where
b is the base
h is the height
From the question
Area = 21 m²
The statement
The height of a triangle is 8 m more than the length of the base is written as
h = 8 + b
Make b the subject
That's
b = h - 8
Substitute the expression into the above formula and solve for the height
That's
[tex]21 = \frac{1}{2} (h - 8)h[/tex]
Multiply through by 2
h² - 8h = 48
h² - 8h - 48 = 0
(h + 4)(h - 12) = 0
h + 4 = 0 h - 12 = 0
h = - 4 h = 12
Since the height cannot be a negative number we have the final answer as
height = 12 cm
Hope this helps you
