Problema Solution
The area of a rectangular athletic field is represented by the expression 9y^2-25z^2 square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution.
Answer provided by our tutors
The area of a rectangle is given by
area = length*width
here the area is given as
area = 9y^2 - 25z^2 square meters
now you can see that 9 = 3^2 and 25 = 5^2
we can rewrite the eqn as
area = (3y)^2 - (5z)^2
this is the diffrence between two square values
we can factorize this as
area = (3y - 5z)*(3y+5z)
so if we take 3y-5z as the length of the field in meters 3y+5z can be taken as the length
width = 3y-5z meters
length = 3y+5z meters