Mathematics

Problem

A triangular roof truss is modeled by

f(x)

on the interval

[-3, 3]

with peak at

(0, 2)

and base vertices at

(-3, 0)

and

(3, 0)

. The truss is raised onto walls of height

h

, transforming the function to

g(x) = f(x) + h

. If the new peak height is

5\,\text{m}

, find the length of the new base segment connecting

(-3, h)

and

(3, h)