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.
I am sorry, How would I set this problem up?
First, you have a right-angle triangle; its height is 2 m and its hypotenuse is 6 m. To find the base, use the Pythagorean theorem: a^2 + b^2 = c^2. This gives you half the length of a piece of insulation. Double that number to find the total length of each piece.
If you post your answer, we'll be glad to check it.
Okay,If I understand this is what I come up with.
square root of 6^2-2^2=x^2
square root of 36-4=x^2
square root of 32=x^2
x=4 square root of 2*2= x=8 square root of 2= approx. 11.3 m
Right! You've got it! :-)
Thanks! :)
To calculate the length of each piece of insulation needed, we need to determine the hypotenuse of a right triangle formed by the roof, the attic space, and the insulation.
Given:
- The peak to eave distance (base) = 6 m
- The height of the attic space (height) = 2 m
Using the Pythagorean theorem, we can find the length of the hypotenuse:
hypotenuse = √(base^2 + height^2)
Let's calculate it:
base^2 = 6^2 = 36
height^2 = 2^2 = 4
hypotenuse = √(36 + 4) = √40 ≈ 6.3 m
Now that we have the length of the hypotenuse, we can determine the length of the insulation pieces. The hypotenuse represents the distance between the rafters in the attic where the insulation will be placed.
Since the insulation comes in 40-cm wide rolls (0.4 m), each piece of insulation needs to be slightly longer than the hypotenuse. We can add a safety margin of around 10 cm (0.1 m) to ensure a proper fit.
Therefore, the length of each piece of insulation needs to be approximately 6.4 meters (6.3 m + 0.1 m).