If the base of a triangle is 4 units longer than twice its height and has an area of 240 square units, how long is the base of the triangle?

The area of the triangle is:

A = (1/2) * (b) * (h)

Where,

b: base

h: height

Substituting values we have:

Where,

b = 2h + 4

h = (1/2) * b-2

Substituting values we have:

240 = (1/2) * (b) * ((1/2) * b-2)

Rewriting:

480 = ((1/2) * b ^ 2-2b)

960 = b ^ 2-4b

b ^ 2-4b-960 = 0

Solving the polynomial:

b1 = 22.93171219946131

b2 = - 20.93171219946131

Using the positive root we have:

b = 22.9 units

Answer:

the base of the triangle is:

b = 22.9 units