SOLUTION: Good afternoon The height of a triangle is two more than three times the base. Determine the dimensions that will give a total area of 28 yds2. What is the minimum area of such a

Algebra ->  Equations -> SOLUTION: Good afternoon The height of a triangle is two more than three times the base. Determine the dimensions that will give a total area of 28 yds2. What is the minimum area of such a      Log On


   

Question 867776: Good afternoon
The height of a triangle is two more than three times the base. Determine the dimensions that will give a total area of 28 yds2. What is the minimum area of such a triangle?
Thanks :D
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x base, y height.
y=2+3x.
%281%2F2%29xy=28
%281%2F2%29x%283x%2B2%29=28
3x%5E2%2B2x=56
highlight_green%283x%5E2%2B2x-56=0%29
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This has only one meaningful solution, and the request that the minimum value be found is not important.
x=%28-2%2Bsqrt%282%2A2-4%2A3%2A%28-56%29%29%29%2F%282%2A3%29
x=%28-2%2Bsqrt%284%2B12%2A56%29%29%2F6
x=%28-2%2Bsqrt%28676%29%29%2F6
x=%28-2%2B26%29%2F6=24%2F6
highlight%28x=4%29, highlight%28y=14%29.

Base is 4 yards and height is 14 yards.