Question 300049
 A triangular area is 12 sq. ft.
 Find the base of the triangular area if the height is 1 ft. less than the base.
:
12=1/2b(b-1)
(12)2=(1/2)2(b)2(b-1)2
Right here you should have:
24 = b^2 - b
b^2 - b - 24 = 0; a quadratic equation
This will not factor, use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this equation, x=b; a=1; b=-1; c=-24
{{{b = (-(-1) +- sqrt(-1^2-4*1*-24 ))/(2*1) }}}
:
{{{b = (1 +- sqrt(1 - (-96) ))/2 }}}
:
{{{b = (1 +- sqrt(97 ))/2 }}}
positive solution
{{{b = (1 + 9.85)/2 }}}
b = {{{10.85/2}}}
b = 5.42 ft is the base
and
4.42 ft is the height
:
:
Check solution by finding the area
A = {{{1/2}}}*5.42*4.42
A = 11.97 ~ 12