SOLUTION: For the home described in exercise 15, 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

Algebra ->  Pythagorean-theorem -> SOLUTION: For the home described in exercise 15, 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      Log On


   

Question 73452: For the home described in exercise 15, 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.
May you please show your work
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Hmmm!
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I don't have your book, but I can picture this problem.
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You are going to put insulation down on the floor of the attic and you know that at its
peak the roof is 3 meters above the attic floor. (At the eaves the roof is at the same level
as the attic floor.
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So what you have is the shape of a right triangle. The 7 meter roof is the hypotenuse
and the 3 meter dimension is one of the legs. You need to find the missing leg.
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The Pythagorean theorem tells you that the square of the hypotenuse (call it "c") equals
the sum of the squares of the two legs of the triangle (call them "a" and "b").
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In equation form this becomes:
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a%5E2+%2B+b%5E2+=+c%5E2
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But we know that c is 7 meters and one of the legs (either a or b) is 3 meters. We need
to find the missing leg. Let's say that "a" is the 3 meter leg. Substitute these
values into the equation to get:
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3%5E2+%2B+b%5E2+=+7%5E2
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Square the numbers and you get:
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9+%2B+b%5E2+=+49
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Subtract 9 from both sides to eliminate 9 from the left side and the equation becomes:
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b%5E2+=+40
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Solve for the missing leg by taking the square root of both sides on a calculator
to find that b = 6.32455532 meters.
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Rounding to the nearest tenth gives you 6.3 meters.
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Now you'll need to do some thinking. This length for the insulation will get you from
the eaves to the midpoint of the roof. Does the drawing indicate that the insulation
is to go across the entire attic floor from eave to eave? If it does, then you will have to
double the above answer and buy pieces of insulation that are 12.6 meters long.
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Hope this helps you to see how to solve this problem.
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