Question

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?

Answer 1

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