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