Application of Quadratic Equations

Question

The base of a triangle is longer than twice its corresponding height by 1 cm. The area of the triangle is 105 cm(square). Find the height of the triangle

Answer 1

height ---- x
base ---- 2x + 1

(1/2)(base)(height) = area
(1/2)(2x+1)(x) = 105
x(2x+1) = 210
2x^2 + x - 210 = 0
(x-10)(2x+21) = 0
x = 10 or x = -21/2 , but obviously x has to be positive, so

x = 10
The height is 10 cm

check:
height is 10
base is 21
area = (1/2)(21)(10) = 105
answer is correct