Question 986511
{{{A=(1/2) bh}}}........correct
{{{48=(1/2 )(2x-4)(x)}}}........correct
{{{48=(1/2) (2x^2-4x)}}}........correct
{{{48=x^2-2x}}}........correct
{{{0=x^2-2x-48}}}........correct

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

 {{{x = (-(-2) +- sqrt( (-2)^2-4*1*(-48) ))/(2*1) }}}

{{{x = (2 +- sqrt( 4+192 ))/2 }}}

{{{x = (2 +- sqrt( 196 ))/2 }}}

{{{x = (2 +- 14)/2 }}}

positive solution:

{{{x = (2 + 14)/2 }}}

{{{x =16/2 }}}

{{{highlight(x = 8) }}}=> this is a height

now find the length of the base
{{{b=2x-4}}}
{{{b=2*8-4}}}
{{{b=16-4}}}
{{{highlight(b=12)}}}=>the base

check:
 
{{{A=(1/2) bh}}}

{{{A=(1/2) 8*12}}}

{{{A=(1/cross(2)1)cross( 8)4*12}}}

{{{A=4*12}}}

{{{A=48}}}



the hypotenuse:

{{{c^2=a^2+b^2 }}}

{{{c^2=8^2+12^2 }}}

{{{c^2=64+144 }}}

{{{c^2=208 }}}

{{{c=sqrt(208) }}}

{{{c=14.42220510185596 }}}

{{{highlight(c=14.4) }}}........must be decimal