Answer:
the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.
Explanation:
Note that the formula for the area of a triangle is A = (1/2)(base)(height). Let's abbreviate that to A = (1/2)(b)(h). We are told that h = b + 8.
Then A = 136.5 = (1/2)(b)(b + 8), or
(after multiplying both sides by 2)
A = 273 = b^2 + 8b
which, when put into standard quadratic form, becomes:
b^2 + 8b - 273 = 0
The coefficients of this quadratic are a = 1, b = 8 and c = -273.
Thus, the discriminant is b^2 - 4ac, or 64 - 4(1)(-273) = 1156 = 17^2.
The roots are then
-8 ± √1156 -8 ± 17
x = -------------------- = ------------ = 9/2 and -25/2
2 2
Only the root 9/2 makes sense here, because measurements of length are positive.
Thus, the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.