Question 113055
the formula for the area of a triangle is:

{{{A = (1/2)b*h}}}

Or

{{{A = b*h/2}}}

Given:

{{{A = 6cm^2}}}

{{{h = 5cm + 3b}}}

Then


{{{A = b*h/2)}}}

{{{6cm^2= b(5cm + 3b) /2}}}

{{{6cm^2 = (5bcm + 3b^2) /2}}}….multiply both sides by {{{2}}}

{{{12cm^2 = 5bcm + 3b^2}}}….


{{{3b^2 + 5bcm  -12cm^2 = 0 }}}….now use sqrt formula to find only positive root


{{{b[1]=(-5 + sqrt (5^2 -4*3*(-12) )) / (2*3)}}}

{{{b[1]=(-5 + sqrt (25 + 144 )) / 6}}}

{{{b[1]=(-5 + sqrt (169 )) / 6}}}

{{{b[1]=(-5 + 13 ) / 6}}}

{{{b[1]= 8  / 6}}}

{{{b[1]= 1.33cm}}}


Then 

{{{h = 5cm + 3b}}}

{{{h = 5cm + 3(1.33cm)}}}

{{{h = 5cm + 3.99cm)}}}

{{{h =  8.99cm)}}}

check:

{{{A = b*h/2}}}

{{{A = (1.33*8.99)/2}}}

{{{A = (11.96)/2}}}

{{{A = 5.98cm^2= 6cm^2}}}