Question 74891: I can't seem to figure out the formula for the following word question. Can you assist? A homeowner wishes t insulate her attic with fiberglass insulation to conserve energy. This insulation comes in 40-cm wide rolls that are cut to fit between the rafters in the attic. If the roof is 6m from peak to eve and the attic space is 2m high at the peak, how long does each of the pieces of insulation need to be?
This is from Basic Algebra as pictured in some of the other questions
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You can solve this problem using the Pythagorean theorem. If you stand in the attic and
drop a plumb line (a vertical line) from the peak of the attic roof down to the floor in
the attic, the length of this line will be 2 meters as the problem tells you. Note that the
string line will be perpendicular to the floor in the attic. So we have a right triangle
formed by the peak of the roof down to the floor of the attic, then horizontally out to the
eave (edge) of the roof, and then slanting back to the peak of the roof. The problem tells
you the dimensions of two of the sides of this triangle. The longest side is the slant
shingled distance from the eave to the peak of the roof and the problem says it is 6m.
One of the short sides (a leg) is the 2 meter length from the peak down to the floor of
the attic. All that we are missing is the horizontal distance from the string line point
on the attic floor directly under the peak of the roof horizontally out to the eave. The
Pythagorean theorem tells us that the sides of a right triangle are related by the equation:
.
.
where c is the hypotenuse or longest side in the triangle. In this problem c equals 6
meters of the slanted, shingled roof. The problem tells you that one of the other sides
is 2 meters. Substitute these two values into the Pythagorean equation to get:
.
.
Square out the known values and you get:
.
.
Get rid of the 4 on the left side by subtracting 4 from both sides and you have:
.
.
Now solve by taking the square root of both sides and you have:
.
 meters.
.
Since I don't have a drawing of the actual house, this could be the insulation length that
the problem asked you to find. Or it might be just half of the insulation length because
If the peak of the roof is only half way across the house, you may want the insulation
to roll from one eave all the way across the house to the opposite eave. So be aware that
you may want to double the answer we got if the peak is midway between the eaves.
.
Also, in real life you don't buy insulation in exact lengths. You buy it cut to fit between
the floor joists (boards) in the attic (in the US generally 16" wide or 24" wide), and
you unroll it into place. When the roll gets to the end, you just open another
roll and
butt it up against the piece you just installed and continue on your way. And when you
come to the eave, you just slice the insulation with a box knife or some similar cutter and
move on to the next empty space between the joists. However, that doesn't make for a
good math problem. And so much for real life!
.
Hope this analysis helps you to understand the problem.
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