How Do You Calculate the Area of a Motel Given Wall Lengths?

[bleedblue1234]

Homework Statement

A small motel is to be built as shown in the sketch with two long walls y feet long each and 6 short walls x feet long each. The total length of the walls is to be 300 feet.

Let A(x) be the number of sq feet area taken up by the motel. Write the particular equation for A(x). What kind of function is this?
y
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| | | | | | x
| | | | | |
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something like that

Homework Equations

y = ax^2 + bx + c

The Attempt at a Solution

no idea where to start

 

[Mark44]

The total length of all of the walls is 300'.
The six short walls define five rectangular regions - count them in your text drawing. What are the dimensions of the width and length of each rectangle?
What is the area of each rectangle?
What is the total area of all five rectangles?

How is y = ax^2 + bx + c a relevant equation?

 

[bleedblue1234]

The total length of all of the walls is 300'.
The six short walls define five rectangular regions - count them in your text drawing. What are the dimensions of the width and length of each rectangle?
What is the area of each rectangle?
What is the total area of all five rectangles?

How is y = ax^2 + bx + c a relevant equation?

yes but it asks for a particular function and i get y*6x and this is not quadratic...

 

[Mark44]

yes but it asks for a particular function and i get y*6x and this is not quadratic...

The problem asks for A(x), meaning a function of just x (no y in it). Since you don't have a function of x alone, you don't know whether the one you really want is quadratic or not. How did you get y*6x as the area?

You haven't taken into account that the total length of all of the walls is 300'.

I'll ask my questions again.
The six short walls define five rectangular regions - count them in your text drawing. What are the dimensions of the width and length of each rectangle?
What is the area of each rectangle?
What is the total area of all five rectangles?

I'll keep asking them until you answer them.

 

[arithmetix]

The quoted equation is called a quadratic, and if your teacher is responsible you'll have notes on how to deal with quadratics. Usually the job is done by formula:


Given a, b, and c

If ax^2+bx+c=0 then:

x=(-b+-(b^2-4ac))/(2a)

 

[Mark44]

The quoted equation is called a quadratic, and if your teacher is responsible you'll have notes on how to deal with quadratics. Usually the job is done by formula:
Given a, b, and c
If ax^2+bx+c=0 then:
x=(-b+-(b^2-4ac))/(2a)

You're waaaaaay ahead of the OP. He/she is still trying to find a formula for the area of the enclosed rectangles. Let's hold off on solving quadratic equations until he/she at least comes up with a function.

 

[bleedblue1234]

The six short walls define five rectangular regions - count them in your text drawing. What are the dimensions of the width and length of each rectangle? w= x and l = y/6
What is the area of each rectangle? x * y/6 or y*6x
What is the total area of all five rectangles? (5)(y*6x) <= 300

haha holy crap i am bad i am sooo sick tonight i can't even think how to add numbers... i am usually very good at this sort of stuff and have done fine on all of the other models...

 

[HallsofIvy]

The quoted equation is called a quadratic, and if your teacher is responsible you'll have notes on how to deal with quadratics. Usually the job is done by formula:


Given a, b, and c

If ax^2+bx+c=0 then:

x=(-b+-(b^2-4ac))/(2a)

Please read questions carefully before you respond. The original post asked only for the area as a quadratic equation. Nothing is said about solving the equation.

 

[Mark44]

The six short walls define five rectangular regions - count them in your text drawing. What are the dimensions of the width and length of each rectangle? w= x and l = y/6

The width is x, yes, but the length of each one is y/5.

What is the area of each rectangle? x * y/6 or y*6x

The area of each rectangle is x*y/5. Note that your answer x*y/6 is NOT equal to y*6x.

What is the total area of all five rectangles? (5)(y*6x) <= 300

No. The area of each rectangle is x*y/5. There are 5 rectangles, so the total area is 5*x*y/5 = ?

haha holy crap i am bad i am sooo sick tonight i can't even think how to add numbers... i am usually very good at this sort of stuff and have done fine on all of the other models...

To summarize, A = 5*x*y/5, which you should simplify. This is the area, but it is not yet a function of x alone. To make it a function of x, you need to work in the other information in this problem, that the total length of the walls, which is 300'.

Look at your drawing and add up the lengths of the 2 walls going across and the 6 walls going up and down. This will give you an equation in x and y.

Solve this equation for y, and substitute for y in your area equation.