Question 129879
Let x=height


Since the "base of a triangular sail is 5m shorter than its height", we have the equality {{{b=x-5}}}


{{{A=(b*h)/2}}} Start with the formula for the area of a triangle



{{{18=((x-5)*x)/2}}} Plug in {{{b=x-5}}}, {{{h=x}}}, and {{{A=18}}}



{{{36=(x-5)*x}}} Multiply both sides by 2



{{{36=x^2-5x}}} Distribute



{{{0=x^2-5x-36}}} Subtract 36 from both sides




{{{0=(x-9)(x+4)}}} Factor the right side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x-9=0}}} or  {{{x+4=0}}} 


{{{x=9}}} or  {{{x=-4}}}    Now solve for x in each case



So our possible answers are

 {{{x=9}}} or  {{{x=-4}}} 



However, since a negative height doesn't make sense, our only solution is {{{x=9}}} 




So the height is 9 m


Now subtract 5 from the height to get the base



{{{b=9-5=4}}}



So the base is 4 m




Check:



{{{A=(b*h)/2}}} Start with the formula for the area of a triangle



{{{18=(4*9)/2}}} Plug in {{{b=4}}}, {{{h=9}}}, and {{{A=18}}}



{{{18=36/2}}} Multiply



{{{18=18}}} Divide. Since the two sides of the equation are equal, this verifies our answer.