
Title:
Grants Fun Office  College Algebra

Description:

Athena started interning at an architecture firm, to learn the basics of

designing and planning for the construction of new buildings. This isn't just

any architecture firm, though. It just so happens to be the firm that designed

the new office for Grant's gleaming glasses company. So we're going to go back

in time to follow Athena through the work that went into creating Grant's

awesome new space. Since Athena is just getting used to being a part of the

world of architecture at all, the firm gave her a pretty simple project to work

on first. Since Grant's such a fun guy, he wanted his office to have a separate

space, just for having fun. Thus, the fun room, which Athena get's to plan.

Grant has picked out a very special wallpaper that he wants used in this room.

And has a pattern that he wants to make sure is fully expressed on every wall,

but he also wants there to be natural light in the room. So he wants windows

along two of the walls. However, since he's not willing to sacrifice any of that

wallpaper pattern, the two walls with the windows on them are going to have to

be longer than the other two walls. Let's call the distance from one wall to the

edge of a window x. And assume that each of these windows are placed in the

center of either wall. So that there's a distance of x on either side. Now,

since Grant loves natural light so much, he wants these windows to be really

big. In fact, he's already picked out, surprise, surprise, the exact windows

that he wants. And they are each 3 meters across. Now, since we're calling each

of these lengths of wall x, we know that this length of wall is going to be

equal to the sum of those two. So this is just 2x. Now, the thing that Athena

needs to figure out is how much carpet is going to need to be laid down in the

fun room. So considering these side links and your understanding of, area of

rectangles, please come up with an expression for the number of square meters of

carpet Athena's going to need for this room. You could either multiply or not

multiply out your answer.