SOLUTION: A triangular sail for a yacht needs to have a surface area of 84m squared. The base length X+8 relative to the vertice height of the sale which is 2x+6 where the value of X in metr

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A triangular sail for a yacht needs to have a surface area of 84m squared. The base length X+8 relative to the vertice height of the sale which is 2x+6 where the value of X in metr      Log On


   

Question 1043163: A triangular sail for a yacht needs to have a surface area of 84m squared. The base length X+8 relative to the vertice height of the sale which is 2x+6 where the value of X in metres is not known. Use your knowledge of quadratic functions to find the value of X and determine the length of the base and the vertical height of the sail.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A triangular sail for a yacht needs to have a surface area of 84m squared.
The base length X+8 relative to the vertical height of the sail which is 2x+6 where the value of X in metres is not known.
Use your knowledge of quadratic functions to find the value of X and determine the length of the base and the vertical height of the sail.
:
The way I understand all this, is a right triangle,
b = (x+8)
h = (2x+6)
:
The area of a right triangle
1%2F2*(x+8)*(2x+6) = 84
multiply both sides by 2, FOIL
2x^2 + 6x + 16x + 48 = 168
2x^2 + 22x + 48 - 168 = 0
2x^2 + 22x - 120 = 0
simplify divide by 2
x^2 + 11x - 60 = 0
Factors to
(x+15)(x-4) = 0
the positive solution is all we want here
x = 4
therefore
4+8 = 12 m is the base
and
2(4)+6) = 14 m is the height
:
:
Check, find the area of the sail with these dimensions:
1%2F2*12*14 = 84 sq/m