Question 874072
Let b = base
Let b+4 = height
{{{1/2*bh=A}}}
{{{1/2*b*(b+4)=160}}}
Distribute
{{{1/2*b^2+2b=160}}}
Subtract 160 from both sides
{{{1/2*b^2+2b-160}}}
Use the quadratic formula, where x = b
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-2 +- sqrt( 2^2-4*1/2*-160))/(2*1/2) }}}
{{{x=-2+-sqrt(4+320)}}}
{{{x=-2+-sqrt(324)}}}
Because the measurements must be positive,
{{{x=-2+18}}}
{{{x=16}}}
The base is 16 and the height is 20.