# 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

Algebra ->  -> 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      Log On

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 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(3556)   (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 ----- the volume of your tent is the area of the face times the length. ----- the face is a triangle. the area of the face is (1/2)bh = (bh)/2 where: b = the base and h = the height. ----- the base is given as (2x+2) units wide. the height is given as (x+1) units high. ----- the area of the face is therefore: /2 ----- this comes out to be k which reduces to: ----- 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. ----- the volume is given as cubic units. ----- we know the area so we have to solve for L. ----- L = V/A ----- The division is shown on page 2 of the notes. The result of the division is L = x+5 units. ----- That's your answer. ----- to doublecheck, take (x+5) and multiply it by (x^2 + 2x + 1) and you'll get the volume of the tent. ----- more information can be found at the following website: http://www.mathsteacher.com.au/year9/ch14_measurement/19_prism/prism.htm -----