testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Active Topics | Members | Search | FAQ
Username:
Password:
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Algebra
 The Attic Insulating Problem.
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

Zubaida
Average Member

Saudi Arabia
13 Posts

Posted - 03/07/2012 :  06:00:43  Show Profile  Reply with Quote

Hello,
Can please answer my questions regarding the following problem?

A homeowner wishes to insulate her attic with fiberglass insulations to conserve energy. The insulation comes in 40-cm wide rolls that are cut to fit between rafters in the attic. If the roof is 6 m from peak to eave and the attic space is 2 m high at the peak, hoe long does each of the pieces of installation need to be? Round to the nearest tenth.

The solution:
To know how long is the the floor of the attic, we apply the Pythagorean theorem (c = a + b). We substitute, 6 = a + 2.
a= 36 - 4
a= 32
a= 32
a= 5.65685424949
a= 5.7m


Is this is the length of each of the pieces of installation? or should I multiply by two to get the true length (the length of the attic floor)?
The insulation comes in 40-cm wide rolls. Is this information is useless. If not? How can I benefit from?


Thank you,
Go to Top of Page

TchrWill
Advanced Member

USA
80 Posts

Posted - 03/07/2012 :  10:14:54  Show Profile  Reply with Quote
A homeowner wishes to insulate her attic with fiberglass insulation to conserve energy. The insulation comes in 40-cm wide rolls that are cut to fit between rafters in the attic. If the roof is 6 m from peak to eave and the attic space is 2 m high at the peak, how long does each of the pieces of installation need to be? Round to the nearest tenth.

Assuming the "6m from peak to eave" is the half-width of the roof surface, the length of each piece of attic floor insulation is sqrt(6^2 - 2^2)2 = sqrt(32)2 = 8sqrt(2)m = 11.3m.

The length of each piece lying between the roof rafters is 12m.

Go to Top of Page

Zubaida
Average Member

Saudi Arabia
13 Posts

Posted - 03/07/2012 :  14:02:53  Show Profile  Reply with Quote
Hello,
I have another question please,
Where will the homeowner put insulations?
If she will put them on the roof, I think there is no need to use the Pythagorean theorem. We multiply 6 by 2 = 12m. Right?

If she will put insulations on the floor, then we should use the Pythagorean theorem to know how long each piece should be (as we solved previously)


Thank you,
Zubaida
Go to Top of Page

the_hill1962
Advanced Member

USA
1469 Posts

Posted - 03/07/2012 :  15:45:45  Show Profile  Reply with Quote
Insulation is put on the floor of the attic since you don't want the heating and cooling loss stopped there. You don't want the heat and cold energy to be heating and cooling the attic space.
Each piece of insulation would be 232. That is 2162 which is 82. It says to round to the nearest tenth so that would be 11.3m.
quote:
Originally posted by Zubaida

Hello,
I have another question please,
Where will the homeowner put insulations?
If she will put them on the roof, I think there is no need to use the Pythagorean theorem. We multiply 6 by 2 = 12m. Right?

If she will put insulations on the floor, then we should use the Pythagorean theorem to know how long each piece should be (as we solved previously)


Thank you,
Zubaida



Edited by - the_hill1962 on 03/07/2012 15:51:08
Go to Top of Page

Zubaida
Average Member

Saudi Arabia
13 Posts

Posted - 03/07/2012 :  16:10:27  Show Profile  Reply with Quote
Thank you TchrWill and the_hill1962 for your explanation.
But why TchrWill said that the length of each piece lying between the roof rafters is 12m. Does he mean that 12 is the result of rounding 11.3 to the nearest tenth? Why not 11m?
Is this because the insulations will not cover all the space if the result is 11m?

Thank you,


Go to Top of Page

the_hill1962
Advanced Member

USA
1469 Posts

Posted - 03/15/2012 :  13:44:45  Show Profile  Reply with Quote
I wondered the same think myself. I do think that is what he meant (11.3 can't be rounded to 11 in this case because it would make a gap----true, not much of one but I suppose it is important for insulation to be snug since there would be a space where cold or hot air can draft in and out).
About the "40cm" information. That is just how wide it is to fit between the rafters. The length is what needed to be calculated. Using 12m assures that you will have enough. You don't want to be short! Say that you buy just enough using the 11.3m figure. Well, as you cut each length, suppose that you weren't exactly at 11.3m each and you made them a little bit more (just to make sure it is fitting in without leaving gaps and not having to stretch it)-----all that extra adds up and your last piece would be short.
It is better to have extra left.
quote:
Originally posted by Zubaida

Thank you TchrWill and the_hill1962 for your explanation.
But why TchrWill said that the length of each piece lying between the roof rafters is 12m. Does he mean that 12 is the result of rounding 11.3 to the nearest tenth? Why not 11m?
Is this because the insulations will not cover all the space if the result is 11m?

Thank you,




Go to Top of Page

TchrWill
Advanced Member

USA
80 Posts

Posted - 03/16/2012 :  14:37:36  Show Profile  Reply with Quote
Thank you TchrWill and the_hill1962 for your explanation.
But why TchrWill said that the length of each piece lying between the roof rafters is 12m. Does he mean that 12 is the result of rounding 11.3 to the nearest tenth? Why not 11m?
Is this because the insulations will not cover all the space if the result is 11m?

Assuming the "6m from peak to eave" is the half-width of the roof surface, the length of each piece of attic floor insulation is sqrt(6^2 - 2^2)2 = sqrt(32)2 = 8sqrt(2)m = 11.3m.

The length of each piece lying between the roof rafters is 12m.

....................B
..................*l
..............*....l
..........*........l
......*............l
._*____________l
A...................C

AB = 6m
BC = 2m
AC = 11.3m

As pointed out, insulation is normally installed between the attic floor rafters. Since it was not specifically stated, and the length of the roof surface was given, the length of both applications was given.


Edited by - TchrWill on 03/19/2012 14:28:01
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.05 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 18 Dec 2014