SOLUTION: A portion of a wall is a right triangle with a height that is 3 feet more than its base. If the area of the triangle is 27 square feet, find the base

Question 346142: A portion of a wall is a right triangle with a height that is 3 feet more than its base. If the area of the triangle is 27 square feet, find the base
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
Area of Triangle = 1/2 Base X Height
=> Let Y = the Base
=> Then Height = Y + 3
=> 27 = 1/2 { Y * ( Y + 3) }
=> 27 = 1/2 { Y^2 + 3Y }
=> 54 = Y^2 + 3Y (Both side multiple by 2 to eliminate the faction)
=> 0 = Y^2 + 3Y - 54
=> 0 = (Y+9)(Y-6)
=> Y = -9 or +6
=> Since the absolute value of Y has to be more than 0 in order for the Triangle to be real
=> Y = +6
=> In Co-ordinate Trigonometry, the + and - sign will mean the direction/co-odination of the triangle
=> Then both -9 and +6 can be the answer for the base.
Answer: Base is 6 feet, Height is 9 feet.

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