Question 858946
Your question was: <i>"A triangular garden has an area of 200ft^2. It's height is 9 ft more than it's base. Find the measure of the base."</i>
 
let b = x
let h = x+9
{{{A=(1/2)bh}}}
{{{200=(1/2)x(x+9)}}}
Distribute the x
{{{200=(1/2)(x^2+9x)}}}
Subtract 200 from both sides
{{{0=(1/2)(x^2+9x)-200}}}
Multiply both sides by 2
{{{0=x^2+9x-400}}}
Plug the values into the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-9 +- sqrt( 9^2-4*1*-400 ))/(2*1) }}}
Do the multiplication
{{{x = (-9 +- sqrt( 81+1600 ))/2 }}}
{{{x = (-9 +- sqrt( 1681 ))/2 }}}
The square root of 1681 is 41.
At this point you have to split it into 2 equations: one where you <b>add</b> 41, and one where you <b>subtract</b> 41. We'll deal with the first one first.
{{{x=(-9+41)/2}}}
{{{x=32/2}}}
{{{x=16}}}
Next, deal with <b>Subtract</b> 41
{{{x=(-9-41)/2}}}
{{{x=(-50)/2}}}
{{{x=-25}}}
Since the base can't be negative, discard -25. 
The base is 16ft.
To check, plug it in to the area formula:
{{{A=(1/2)bh}}}
{{{A=1/2*16*25}}}
{{{A=200}}}
Your checked answer is 16 feet long.