SOLUTION: A tent has the shape of a triangular prism. The volume of the tent is (x^3+7x^2+11x+5) cubic units. The triangular face of the tent is (2x+2) units wide by (x+1) units high. How lo

Question 205242This question is from textbook Advanced Functions & Introductory Calculus
: A tent has the shape of a triangular prism. The volume of the tent is (x^3+7x^2+11x+5) cubic units. The triangular face of the tent is (2x+2) units wide by (x+1) units high. How long is the tent? This question is from textbook Advanced Functions & Introductory Calculus

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
hand written notes and a picture can be found at the following website:
http://theo.x10hosting.com/
just click on 205242.1 and 205242.2
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the volume of your tent is the area of the face times the length.
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the face is a triangle.
the area of the face is (1/2)bh = (bh)/2 where:
b = the base and
h = the height.
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the base is given as (2x+2) units wide.
the height is given as (x+1) units high.
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the area of the face is therefore:
/2
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this comes out to be k which reduces to:

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the volume for this type of a triangular prism is:
V = A*L
where A is the area of the face and L is the length of the tent.
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the volume is given as cubic units.
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we know the area so we have to solve for L.
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L = V/A
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The division is shown on page 2 of the notes.
The result of the division is L = x+5 units.
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That's your answer.
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to doublecheck, take (x+5) and multiply it by (x^2 + 2x + 1) and you'll get the volume of the tent.
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more information can be found at the following website:
http://www.mathsteacher.com.au/year9/ch14_measurement/19_prism/prism.htm
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