The rectangle poster shown at the right measures 2w-30 by w. the poster has an area of 5400 cm^2. what is the value of a?

This is the concept of algebra, to get the values of the unknown we proceed as follows:
Length=(2w-30) cm
width=w
Area=length×width
=w(2w-30)=5400
=2w^2-30w=5400
hence
2w^2-30w-5400=0
solving the quadratic we get:
w^2-15w-2700=0
thus
(w+45)(w-60)=0
hence
w=-45 or w=60
since there is no negative dimension we shall take w=60
thus the value of w=60

24 is the correct answer.