Question 746903
Let x represent the length of the base.

Then the height can be represented as {{{h=2x+5}}} (5 units more than twice the base)

Now, the formula for the area of a triangle is {{{A=b*h}}}

So, {{{21=(1/2)*x*(2x+5)}}}

Using the distributive property,
 {{{21=x^2+(5/2)x}}}

Subtract 21 from both sides, 

{{{0=x^2+(5/2)x-21}}}

Now, using a=1, b=5/2, and c=-21, plug into the quadratic formula.

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{x = (5/2 +- sqrt( (5/2)^2-4*(2)*(-21 )))/(2*(2)) }}}


{{{x = (2.5 +- sqrt( 6.25+168 ))/4 }}}


{{{x = (2.5 +- sqrt( 174.25 ))/4 }}}


There are two possible answers.  {{{x=(2.5+ sqrt( 174.25 ))/4}}} or {{{x=(2.5- sqrt( 174.25 ))/4}}}

The second answer would result in a negative number.  Since we are trying to find out the length of the base of a triangle, we can throw out the negative answer.  

Thus, {{{x=(2.5+ sqrt( 174.25 ))/4}}}

So x is about 3.925 units.  

x was representing the base.  Since the height was 2x+5, simply plug in the x value found above to find the height.
{{{h=2x+5}}}
{{{h=2*(3.925)+5}}}
{{{h=7.850+5}}}

h=12.850 units