Question 120877
{{{A=((a-1)((a+7)+8))/2}}}
{{{A=((a-1)(a+15))/2}}}
{{{A=(a^2+14a-15)/2}}}



You have an expression in terms of the variable a that represents the area, so all you need to do is set that expression equal to 25 and solve.


{{{A=(1/2)a^2+7a-(15/2)}}}


{{{(1/2)a^2+7a-(15/2)=25}}}


Since fractional coefficients will be a pain when you evaluate the quadratic formula, multiply through by 2:


{{{a^2+7a-15=50}}}


Now add -50 to both sides to get the equation in standard form:


{{{a^2+14a-65=0}}}


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-14 +- sqrt( 14^2-4*1*(-65) ))/(2) }}} 
{{{x = (-14 +- sqrt( 456 ))/(2) }}} 
{{{x = (-14 +- 2sqrt( 114 ))/(2) }}} 
{{{x = -7+- sqrt( 114 ) }}}


{{{-7-sqrt(114)}}} can be excluded because it is clearly less than zero and the problem conditions demand a > 1.  So the correct and only answer is:


{{{x=-7+sqrt(114)}}}, roughly 3.7


Should you believe me?  Not without checking, you shouldn't.


{{{A=(((-7+sqrt(114))-1)(((-7+sqrt(114))+7)+8))/2}}}
{{{A=(sqrt(114)-8)(sqrt(114)+8)/2=(114-64)/2=50/2=25}}} Answer checks