Question

a simple pendulum has a period of 4.50secs,when the length is shortened by 1.2m the period is 2.50secs. calculate the original length of the pendulum

Answer 1

Recall that T = 2π√(L/g)
so, L = (4.5/(2π))^2 * 9.81 = 5.03 m

was there some other value of g you wanted to use, making it necessary to consider the shorter pendulum?

Let's see what we'd do if we didn't know g.
T = 2π√(L/g)
T^2/L = 4π^2/g, which is constant. In that case, you want L such that
4.5^2/L = 2.5^2/(L-1.2)
That gives L = 1.74 m