Question 21412
let  h = the height
let b = the base
let A = the area

A = 16 = (1/2)*b*h

multiply each side by 2
(a) 32 = b*h

from the description of the problem, 
b = 3*h - 4
substitute this result for b into (a)
{{{32 = (3*h - 4)*h}}}
{{{32 = 3*h^2 -4*h}}}
rearranging,
(b) {{{3*h^2 - 4*h - 32 = 0}}}
this is a quadratic equation
the roots (negative and positive) are given by
{{{ (-b +-sqrt(b^2 - 4*a*c))/(2*a)}}}
if the form of the equation is
a*h^2 + bh + c = 0
from our result in (b), 
a = 3
b = -4
c = -32

{{{(-(-4) +- sqrt(16 - (4 *3*(-32))))/(2*3)}}}
{{{(4 +- sqrt(16 + 384))/6 }}}
{{{(4 +- sqrt(400))/6 }}}
{{{(4 +- 20)/6 }}}
choose the positive result
{{{(4 + 20)/6 }}}
{{{4 = r1}}}
therefore h = 4
32 = b*h
b = 32/4
b = 8
substitute these values back into
b = 3*h - 4
A = (1/2)*b*h