Applications of the Pythagorean Theorem (insulation)

[Katie1]

I thought I was getting this untill I hit the word problem. I have the hardest time setting them up and doing it correctly. It is not one of my homework problems, and I do have the answer to it but I can not get the correct answer. Here is my problem:

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 the 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 insulation need to be? Round to the nearest tenth.

This is what I have...

x=the squart root of 6^2-2^2

x=the square root of 36-4

x= the square root of 32

this is where I am lost..well if i am even doing it correctly.

 

[Loren]

If I understand the problem I think your work so far is correct. Are you assuming that the roof only slopes in one direction? In other words, are there two right triangles involved in your sketch so that you need to multiply your result so far by two?

 

[soroban]

Hello, Katie!

The problem is not stated clearly . . .

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 the 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 insulation need to be?
Round to the nearest tenth.

The end view of the attic seems to look like this:

                        *
                     *  |  *
                  *     |     *   6
               *       2|        *
            *           |           *
         *              |              * 
      * * * * * * * * * * * * * * * * * * *
      : - - -  x  - - - : - - -  x  - - - +

The problem should have specified what part of the attic is to be insulated.

If the "ceiling" is to be insultated, then the length will be 6 meters, of course,
. . and the 2-meter height is unnecessary.

So I would GUESS we are to cover the floor of the attic.
Then we need to find the length of \(\displaystyle x\).
And the required length will be \(\displaystyle 2x.\) meters.

If that is the case, your work is correct!

We have: \(\displaystyle \:x^2\,+\,2^2\:=\:6^2\;\;\Rightarrow\;\;x^2\:=\:32\;\;\Rightarrow\;\;x \:=\:\sqrt{32}\:=\:4\sqrt{2}\)

Therefore, the length will be: \(\displaystyle \:2x\:=\:2(4\sqrt{2}) \:=\:8\sqrt{2}\) meters.

 

[Denis]

To teach a student how to calculate the base of an isosceles triangle
given the equal sides and the height by bringing in an attic, rafters
and 40cm rolls makes me shake my head in fake amazement...

 

[Katie1]

Thanks, I finally came up 8 times the square root of 2, which was 11.3 meters