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 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. 
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The way I understand all this, is a right triangle, 
b = (x+8)
h = (2x+6)
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The area of a right triangle
{{{1/2}}}*(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
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Check, find the  area of the sail with these dimensions:
{{{1/2}}}*12*14 = 84 sq/m