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 7 m from peak to eave and the attic space is 3 m high at the peak, how long does each of the pieces of insulation need to be? Round to the nearest tenth.
the formula i need to us for this
if i am correct
7^2m-3^2m=40m
am i corect with this
That is the right formula, however, you failed to take the square root of 40.
length=sqrt(40) meters.
7^2m-3^2m=40^2m
49m-3^2m=40^2m
49m-9m=40^2m
40m=40^2m
40m=1600m
I'm sorry, but your calculations are incorrect. Let's go through the correct steps to find the length of each piece of insulation.
First, we need to determine the length of the horizontal distance between the peak and eave of the roof. We can use the Pythagorean theorem to calculate this.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (in this case, the horizontal distance from peak to eave) is equal to the sum of the squares of the other two sides.
So, using the formula:
a^2 + b^2 = c^2
Where:
a = height of the attic space (3 m)
c = horizontal distance from peak to eave (unknown)
b = half the width of the insulation roll (40 cm / 2 = 20 cm = 0.2 m)
Plugging in the values:
(0.2)^2 + (3)^2 = c^2
0.04 + 9 = c^2
9.04 = c^2
To find c, we take the square root of both sides:
c = sqrt(9.04)
c ≈ 3.01 m
So, the horizontal distance from peak to eave is approximately 3.01 meters.
Now, we can find the length of each piece of insulation by subtracting the width of the insulation roll from the horizontal distance:
length = 3.01 m - 0.4 m (40 cm = 0.4 m)
length ≈ 2.61 meters
Therefore, each piece of insulation should be approximately 2.61 meters long.