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