Question 888499
{{{A=(1/2)bh=(1/2)((1/3)h)h=56}}}
{{{h^2=336}}}
{{{h=sqrt(336)=4sqrt(21)}}}
{{{b=(1/3)(4sqrt(21))=(4/3)sqrt(21)}}}
The other side is the hypotenuse of a right triangle formed by (1/2) the base and the height. Use the Pythagorean theorem.
{{{S^2=(b/2)^2+h^2}}}
{{{S^2=((2/3)sqrt(21))^2+336}}}
{{{S^2=(4/9)21+336}}}
{{{S^2=84/9+3024/9}}}
{{{S^2=3108/9}}}
{{{S=sqrt(3108)/3=(2/3)sqrt(777)}}}
Then,
{{{P=2S+b}}}
{{{P=(4/3)sqrt(777)+(4/3)sqrt(21)}}}
{{{P=(4/3)(sqrt(777)+sqrt(21))}}}