SOLUTION: A triangular sail has an area of x^2 + 5x +6 square meters and a height of x + 3 meters. Find the length of the sail’s base. I have worked this problem 3 times and have come up wit

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Question 140925This question is from textbook UoP Special Edition Elementary and Intermediate Algebra
: A triangular sail has an area of x^2 + 5x +6 square meters and a height of x + 3 meters. Find the length of the sail’s base. I have worked this problem 3 times and have come up with 3 different answers. I know that A=1/2bh. So in this problem A= x^2 + 5x +6, so x^2 + 5x +6 = 1/2b(x+3). So I multiply both sides of the equation by 2 to remove the fraction. This results in 2x^2 + 10x + 12 = b(2x+6). Then I divided both sides by (2x+6). This is where I start having problems. The latest answer I got is x+3+-(6 over 2x+6)=b. I hope this all makes sense, since I can't format it the way it should look. Any help would be greatly appreciated.
This question is from textbook UoP Special Edition Elementary and Intermediate Algebra

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
A triangular sail with an area of: A+=+x%5E2%2B5x%2B6 square meters and a height of: h+=+x%2B3meters, find the length of the sail's base.
Starting with the formula for the area of a triangle:
A+=+%281%2F2%29bh Solve for b. Multiply both sides by 2.
2A+=+bh Divide both sides by h.
b+=+2A%2Fh Make the appropriate substitution:
b+=+2%28x%5E2%2B5x%2B6%29%2F%28x%2B3%29 Simplify.
b+=+%282x%5E2%2B10x%2B12%29%2F%28x%2B3%29 Perform the indicated division.
b+=+2x%2B4
Check:
A+=+%281%2F2%29bh
x%5E2%2B5x%2B6+=+%281%2F2%29%282x%2B4%29%28x%2B3%29 Use FOIL to multiply the binomials.
x%5E2%2B5x%2B6+=+%281%2F2%29%282x%5E2%2B6x%2B4x%2B12%29 Simplify the right side.
x%5E2%2B5x%2B6+=+%281%2F2%29%282x%5E2%2B10x%2B12%29 Perform the indicated multiplication.
x%5E2%2B5x+%2B6+=+x%5E2%2B5x%2B6 Check!