Benjamin C. answered • 06/09/20
Economics Grad Student; Former TA; Math, Writing, Physics
We are given the area the rectangle (22) and the perimeter (24). We also know that for any rectangle, the following two equations must hold true:
(1) perimeter = 2*x + 2*y = 24
(2) area = x*y = 22
We have two equations and two variables to solve for. Remember that x and y in the equations above represent each side of the rectangle, which are the dimensions that the problem asks us to solve for.
It is a bit difficult to work through the math in this text format, but I will start it off for you and hopefully you will be able to figure out the rest on your own:
First, we want to express x in terms of y. We will use equation (1) to do so, which can be rewritten as:
(3) x = 12 - y
Next, we can substitute equation (3) into equation (2) which gives us:
(4) (12 - y) * (y) = 22
We can then use the quadratic formula to solve for y in equation (4). Once we solve for y, its value can be substituted into equation (1) or (2) to solve for x. Hopefully this helps explain how to approach the problem and gives you a head start on solving it!
